U DUALITY

Unofficial Higgs combined plots are in

2011-12-13T11:23:00.000-08:00

As promised, Philip Gibbs has produced combined plots for the Higgs mass, which includes data from LHC, Tevatron and LEP. Notice that nice peak centered at 124-125 GeV!

If this is a light E6 GUT Higgs, we'd expect to see a light isosinglet quark such as the D quark at the LHC very soon. We should even be able to predict its mass (~>250 GeV). A Z' boson would also be nice. For more info, see slides here and here. On to 2012!

Higgs rumors were correct

2011-12-13T07:37:00.000-08:00

The official results are in, at least for the LHC's 2011 data, and it appears the rumors were quite accurate. See TRF and QDS for further details. To quote CMS member Dorigo, who stated there is now "Firm Evidence" with the current data,

So the summary is that ATLAS has a 3.6-sigma significance at 126 GeV, by combining their three most sensitive channels; CMS has a 2.4-sigma significance at 124 GeV, by combining all the meaningful search channels -even less sensitive ones.

After an ATLAS and CMS combined plot is produced, there might very well be over 4 sigma evidence for a light Higgs. I'm certain Philip Gibbs is working on a combined plot at this very moment. There is still a Christmas present to be delivered! Stay tuned.

Why a light Higgs is cool

2011-12-12T22:44:00.000-08:00

As to why many theorists are excited over news of a possible light Higgs boson with 125 GeV mass, here's a memorable excerpt from a September 2011 interview with Clerk Maxwell Professor of Theoretical Physics and former CERN staff member John Ellis:

In the first scenario (114-135 GeV), we could be looking at a Standard Model Higgs boson. This range has been refined experimentally: recent LHC results presented in Mumbai excluded the Standard Model Higgs from about 135 GeV to about 500 GeV, while LEP had previously excluded it up to 114GeV. That leaves a narrow low-mass range of about 20 GeV where it could lie. But if found in this range, the Standard Model theory would still be incomplete; the present electroweak vacuum would be unstable for such a light Higgs in the Standard Model, so we would have to come up with new physics to stabilise it.

Higgs Candidate Events

2011-12-12T13:25:00.000-08:00

While there has been no official announcement on the possible Higgs mass from CERN, there are some nice images available on possible candidate events where the Higgs might have appeared, as mentioned at TRF.

Candidate events in the CMS Standard Model Higgs Search using 2010 and 2011 data (Click images to enlarge)

A typical candidate event including two high-energy photons whose energy (depicted by red towers) is measured in the CMS electromagnetic calorimeter. The yellow lines are the measured tracks of other particles produced in the collision.

A typical candidate event including two high-energy photons whose energy (depicted by red towers) is measured in the CMS electromagnetic calorimeter. The yellow lines are the measured tracks of other particles produced in the collision. The pale blue volume shows the CMS crystal calorimeter barrel.

Real CMS proton-proton collision events in which 4 high energy electrons (green lines and red towers) are observed. The event shows characteristics expected from the decay of a Higgs boson but is also consistent with background Standard Model physics processes.

Real CMS proton-proton collision events in which 4 high energy muons (red lines) are observed. The event shows characteristics expected from the decay of a Higgs boson but is also consistent with background Standard Model physics processes.

Higgs rumors at 124.6 GeV

2011-12-09T16:06:00.000-08:00

December 13 comes ever closer and the rumors about the Higgs mass get more detailed. Lubos Motl has commented on a recent post at QDS by Tommaso Dorigo in which he seems to hint at a possible Higgs mass from diphoton Higgs decay channels

- gamma: a gamma-ray is a photon, i.e. a quantum of light. A very energetic one, to be sure: a gamma ray is such only if it carries significantly more energy than a x-ray, so above a Mega-electron-Volt or so. The gammas we will be hearing about are those directly coming from a Higgs boson decay, and these have an energy of 62.3 GeV, equivalent to the kinetic energy of a mosquito traveling at 9 centimeters per second.

Here, the Higgs mass 124.6 GeV = 62.3 GeV x 2, from a process that can be written as H -> gamma gamma - where the Higgs decays to two high energy photons. Of course, Tommaso admits

I teased my most gullible readers with a (wrong) covert give-away of the Higgs mass ...

Either way, it is fun to speculate when the actual announcement is only a few days away. So let's see how close this 124.6 GeV is to the official (statistical) CMS value on Monday.

Higgs rumors at 125 GeV

2011-12-02T17:04:00.000-08:00

As we all await CERN's official CMS and ATLAS results for the 2011 Higgs hunt, rumors about its mass have surfaced at notable blogs such as Philip Gibbs' viXra log, Peter Woit's Not Even Wrong and Tommaso Dorigo's Quantum Diaries Survivor. As mentioned by "Alex" in the viXra comment section,

Today rumour is: Higgs at 125 Gev around 2-3 sigma…

Such a rumor, if true, would not only indicate evidence for the existence of the Higgs boson, but is evidence for a light Higgs boson (115-135 GeV), which popular models such as E6 GUTs and M-theory on G2-manifolds predict. Of course, 2-3 sigma evidence isn't really conclusive but it does favor physics beyond the Standard Model. These are exciting times and by December 12 and 13 we'll all get to see if the rumors are true. Moreover, Philip Gibbs has also promised everyone a combined CMS and ATLAS plot once the data is released. How's that for an early Christmas present?

Update: Over at Lubos Motl's TRF blog, a commenter "azerty13" said he received the following email from CERN Director General Rolf Heuer:

Dear colleagues,

I would like to invite you to a seminar in the main auditorium on 13 December at 14:00, at which the ATLAS and CMS experiments will present the status of their searches for the Standard Model Higgs boson. These results will be based on the analysis of considerably more data than those presented at the Summer conferences, sufficient to make significant progress in the search for the Higgs boson, but not enough to make any conclusive statement on the existence or non-existence of the Higgs. The seminar will also be webcast.

Rolf Heuer

Such an email, if genuine, definitely supports the 2-3 sigma portion of the 125 GeV Higgs mass rumor. Stay tuned.

Update: As mentioned at viXra log, the latest incarnation of the rumor at Woit's blog gives 3.5 sigma in ATLAS and 2.5 sigma in CMS which amounts to about 4.3 sigma combined for the 10/fb. Keep in mind 5 sigma evidence is what is required at this stage of the Higgs hunting game.

M-theory 11/11/11

2011-11-11T09:49:00.000-08:00

With so many 11's around today, it seems fitting to mention some M-theory related material. A few days ago, Hisham Sati updated his On the geometry of the supermultiplet in M-theory paper which argues that the massless supermultiplet of D=11 supergravity can be generated from the decomposition of reps of the exceptional Lie group F4 and its maximal compact subgroup Spin(9). The dynamical origin of this is proposed to result from Cayley plane bundles over eleven-dimensional spacetime.

The Cayley plane, OP^2, is a projective plane over the octonions and its isometries form the group F4. Lines in OP^2 are 8-spheres and given any two points in OP^2 there is a unique 8-sphere passing through them. Given any three distinct points, if we apply an F4 transformation that fixes one of the points, we get a Spin(9) transformation.

In matrix parlance, F4 is the automorphism group of the algebra of 3x3 Hermitian matrices over the octonions, the exceptional Jordan algebra J(3,O). We can construct OP^2 using the rank one projectors of J(3,O). It can actually be defined as the space of all such rank one projectors. Normalizing the rank one projectors turns them into primitive idempotents, that is, matrices P that satisfy P^2=P which cannot be decomposed as an orthogonal sum of other idempotents. As the identity matrix of J(3,O) is just a 3x3 matrix with ones on the diagonal, its straightforward to see that it decomposes into an orthogonal sum of three primitive idempotents. This is called the capacity and is why J(3,O) is an algebra of degree three.

Going back to the geometry of OP^2, the three distinct points mentioned earlier can be interpreted as three orthogonal primitive idempotents of J(3,O) with orthogonality being a result of these matrices satisfying P1.P2=0 under regular matrix multiplication. To simplify the picture, let's just imagine applying an F4 transformation on the identity matrix where we want to keep one of the diagonal ones fixed. This can be done with a Spin(9) transformation. Since we can fix any of the three diagonal ones of the identity matrix, there are three copies of Spin(9) inside F4 we can use. This freedom of choice we have is what some people refer to as triality.

Creation of Matter and E7

2011-11-03T07:19:00.000-07:00

Recently, Ferrara and Kallosh posted a paper on arxiv entitled Creation of Matter in the Universe and Groups of Type E7. The abstract is as follows:

We relate the mechanism of matter creation in the universe after inflation to a simple and universal mathematical property of extended N > 1 supergravities and related compactifications of superstring theory. We show that in all such models, the inflaton field may decay into vector fields due to a nonminimal scalar-vector coupling. This coupling is compulsory for all scalars except N=2 hyperscalars. The proof is based on the fact that all extended supergravities described by symmetric coset spaces G/H have duality groups G of type E7, with exception of U(p,n) models. For N=2 we prove separately that special geometry requires a non-minimal scalar-vector coupling. Upon truncation to N=1 supergravity, extended models generically preserve the non-minimal scalar-vector coupling, with exception of U(p,n) models and hyperscalars. For some string theory/supergravity inflationary models, this coupling provides the only way to complete the process of creation of matter in the early universe.

As mentioned in the article, one can consider d=4, N=8 supergravity arising from M-theory on T^7, with duality group G=E7(7) acting on a 56-dimensional Freudenthal triple system (FTS) over the split-octonions. Another type arises from the N=2 magic supergravity based on the FTS over the octonions, with duality group G=E7(-25). At an algebraic level, E7(7) and E7(-25) are unified in the complexified duality group G=E7(C) acting on the FTS over the bioctonions. There is, however, no corresponding E7(C) supergravity theory at this time.

Dilogarithm Motives in Physics

2011-09-09T08:17:00.000-07:00

Click Here for Talk

About this episode

Spencer Bloch

"Dilogarithm Motives Arising in Physics"

Talk given at "Algebraic Geometry, K-theory, and Motives" (a conference dedicated to Andrei Suslin's 60th birthday) St. Petersburg, Russia June 25-29, 2010.

In this very clear talk, Bloch explains how one is often writing down interesting periods on n-dimensional projective space when doing high energy physics. One can start with a hypersurface defined by the vanishing of a certain configuration polynomial F of degree d. F determines the hypersurface X, and X determines the motive.

Harmony of Scattering Amplitudes

2011-05-17T07:11:00.000-07:00

The KITP program The Harmony of Scattering Amplitudes is still underway and there have been many wonderful talks on the geometry of scattering amplitudes in twistor space. The twistor approach allows one to look at scattering processes in a more algebraic geometrical fashion where as Ed Witten noted (arXiv:hep-th/0312171), one should focus on holomorphic curves.

At the most basic level, one is interested in degree one genus zero curves. In the complex case, such curves are copies of CP^1, 2-spheres. Witten argued that n-particle MHV amplitudes with two particles of negative helicity and n-2 with positive helicity localize on such degree one genus zero curves. This is the special case of Witten's more general conjecture that the twistor version of the n particle scattering amplitude is nonzero only if the points are supported on an algebraic curve in twistor space of degree d=q-1+l (where q is number of negative helicity particles and l is the number of loops). So for example, the tree level ++--- amplitude is nonzero on a curve of degree d=2-1+0=1, a degree one genus zero curve, a 2-sphere, as expected (see diagram above).

More recently, there is a more combinatorial way to view the MHV (and N^kMHV) amplitudes. This approach allows one to use associahedra, bubble diagrams and chorded polygons, for example. Below is a chorded polygon for the ++--- amplitude, and up to rotation and CPT transformation, is the only one contributing to the amplitude. For the --+++ amplitude there is another such polygon, so for the n=5 MHV amplitudes only (2(n-3))!/(n-3)!(n-2)!=2 total chorded polygons contribute.

In such chorded polygons the chords physically correspond to twistor fields exchanged between degree one genus zero instantons. So given an n-point N^kMHV amplitude, one can draw many different chorded polygons (given by Catalan number C_{n-2}), but those which contribute are those that have no internal twistor field triangles, and describe configurations where each genus zero curve in the process has at least two points with different helicities. Below is a diagram for a non-contributing chorded polygon for the n=8 NNMHV amplitude (note the "illegal" internal twistor field triangle).

As Nima Arkani-Hamed has noted, the twistor approach to scattering amplitudes is revealing a deeper mathematical unity that Feynman diagrams obscure. The mathematics so far involves the Riemann moduli space of surfaces of genus g with n marked points, Gromov-Witten invariants, symplectic geometry, quantum cohomology and motives.

QM over Split Composition Algebras

2011-04-05T09:48:00.000-07:00

Over at viXra log, Philip Gibbs had a nice post on quantum mechanics and non-locality. In traditional quantum mechanics, it is often assumed one is constructing projective spaces over the complex field. However, as John Baez has noted at the n-category cafe, one can always formulate quantum mechanics over the quaternions and octonions as well. In order for octonionic quantum mechanics to be properly formulated, the Jordan formulation must be used in order to define projective spaces. Even then, one is limited to constructing a projective plane in the best case, due to algebraic topological constraints.

Back in my undergrad days, I was interested in studying quantum mechanics over arbitrary division algebras, which inevitably leads to the study of Jordan algebras as normed spaces over the reals. In the octonionic case, first studied by Jordan, Wigner and von Neumann back in the 1920's, one can have an algebra of 3x3 Hermitian operators in the maximal case. This case yields the exceptional Jordan algebra, with its corresponding projective space OP^2, the Cayley-Moufang plane. Even in this somewhat pathological case, it is possible to construct a 27-dimensional normed vector space over the reals. This is done by defining an inner product on the exceptional Jordan algebra, (X,Y)=tr(XoY), which induces a positive definite form, the norm, (X,X)=tr(X^2)=|X|^2. This norm also works for any nxn Jordan algebras over R,C,H. In all these cases, the length of a Hermitian operator is zero if and only if it's the zero vector (zero matrix). This means, in particular there are no rank one operators with zero length, and hence our projective spaces as manifolds, are easily described with the number of charts given by the degree of the Jordan algebra. In quantum mechanics this means we can normalize our rank one operators and the norm squared acquires a nice probabilistic interpretation.

When one attempts to give a similar normed space construction for Jordan algebras over the split composition algebras, it turns out the story isn't so nice. The first property that goes out the window is positive definiteness. So in quantum mechanics over split composition algebras there are a bunch of rank one projectors that have zero length. To this, one may say, "so what?" Well, for one, one can't assign a probabilistic interpretation to pure states described by these vectors. Now one may reply, "so just mod these out and define your projective space accordingly" Sure, we can try to do this but what if the physics actually requires the use of these pathological rank one operators?

Quantum mechanics over split composition algebras has already found use in M-theory compactifications, especially in describing extremal black hole charge vectors. In M-theory on T^5 and T^6, the charge vector spaces are actually Jordan algebras over the split octonions. In the black hole context, rank one operators describe 1/2 BPS states with zero entropy. This can be seen by noting rank one operators are those with zero determinant. So what does the (semi)norm mean in this context? I'm not really sure yet. In a literal sense, it gives the distance squared of an operator from the zero matrix. If one borrows some terminology from D-brane constructions, perhaps the norm can be interpreted as giving a type of tension, proportional to some theoretical mass. This would give an interpretation to the non-trivial charge vectors with zero norm: they describe some type of "massless" 1/2 BPS black holes. The other non-zero norm, rank one charge vectors describe "massive" 1/2 BPS black holes. The spectral decomposition of a full rank 3x3 Hermitian operator in the charge space then says that a 1/8 BPS black hole can be viewed as a bound state of elementary massive 1/2 BPS black holes, in some sense.

FBI can't crack code. Can you?

2011-03-31T16:17:00.000-07:00

For those interested in a cryptographical challenge, the Feds are asking for help on the cracking of a code written by Ricky McCormick, 41, three days before he was found dead on June 30th, 1999 in a St. Louis field.

"We are really good at what we do," said Dan Olson, the chief of the FBI's Cryptanalysis and Racketeering Records Unit. "But we could use some help with this one."

Read more on the challenge at MSNBC.

Is N=8 Supergravity Finite?

2011-03-31T15:08:00.000-07:00

In a recent paper arXiv:1103.4115 [hep-th], Renata Kallosh shows that E7(7) U-duality predicts the all-loop UV finiteness of perturbative N=8 supergravity.

Automorphic Instanton Partition Functions on Calabi-Yau Threefolds

2011-03-08T13:27:00.000-08:00

Persson posted a nice paper recently, exploring the relationships between Calabi-Yau threefolds, U-duality groups and automorphic instanton partition functions. The paper discusses recent attempts at describing the moduli space in type IIA/B string theory on X×S^1, or the hypermultiplet moduli space in type IIB/A on X. It is well known that in certain classes of N=2 supergravities (e.g. magic supergravities) one can use automorphic techniques to constrain quantum corrections. Given a D=3 U-duality group G_3(Z), BPS-degeneracies are recovered from the Fourier coefficients of its related automorphic forms. From this stems the conjecture that the instanton partition function in N=2 supergravity on R^3×S^1 should correspond to an automorphic representation in the quaternionic discrete series of G_3.

arXiv:1103.1014[hep-th]

Abstract: We survey recent results on quantum corrections to the hypermultiplet moduli space M in type IIA/B string theory on a compact Calabi-Yau threefold X, or, equivalently, the vector multiplet moduli space in type IIB/A on X x S^1. Our main focus lies on the problem of resumming the infinite series of D-brane and NS5-brane instantons, using the mathematical machinery of automorphic forms. We review the proposal that whenever the low-energy theory in D=3 exhibits an arithmetic "U-duality" symmetry G(Z) the total instanton partition function arises from a certain unitary automorphic representation of G, whose Fourier coefficients reproduce the BPS-degeneracies. For D=4, N=2 theories on R^3 x S^1 we argue that the relevant automorphic representation falls in the quaternionic discrete series of G, and that the partition function can be realized as a holomorphic section on the twistor space Z over M. We also offer some comments on the close relation with N=2 wall crossing formulae.

Ferrara: Black Holes and Supergravity

2011-03-07T23:06:00.000-08:00

Part I: The Attractor Mechanism

Part II: N=8 Supergravity and Black Hole Charge Orbits

November 10, 2010
Lectures given for 25th Anniversary of ICTP's Dirac Medal, ICTP, Trieste, Italy.

Universe as Black Hole Quantum Computer

2011-02-09T10:03:00.000-08:00

In my last post I entertained the idea of a possible M-theoretical computronium. By definition, computronium is a programmable substrate which can model virtually any object. So M-theory computronium is a realization of such a hypothetical substrate, using objects from M-theory. Along these lines, using the qudit/qubit correspondence, M-theory computronium would essentially be a substrate of programmable extremal black holes. So is an M-theory universe ultimately just a large-scale black hole quantum computer?

Leading researchers such as Seth Lloyd and David Deutsch have argued that the universe, as a giant quantum mechanical system, is indistinguishable from a big quantum computer. Lloyd has stated [1] that since all elementary particles and their interactions register and process quantum information, the universe is constantly performing quantum computations. Moreover, since elementary particles such as the electron and photon can be mapped to qubits and qutrits, their interactions can be seen as the result of quantum logic operations, i.e., quantum computational gates. Hence, the collection of all such qudit computations is indistinguishable from the universe itself.

The arguments by Lloyd and Deutsch are convincing, but from the perspective of string/M-theory we can go one step further, and note that all elementary particles actually arise from more fundamental higher-dimensional objects. In string theory, the popular explanation was that all elementary bosons and fermions arise from vibrations of a string. However, in 1995, after Edward Witten showed that the five known, consistent superstring theories are related by dualities, and it became clear that there was a deeper theory in 11-dimensions, called M-theory that was behind it all. Such a theory, at low energies becomes the unique D=11 supergravity, and contains (among other things) two-dimensional and five-dimensional branes (M2-branes and M5-branes), but no strings. So, from an M-theory perspective all elementary particles should arise from objects in eleven-dimensions, such as the M2 and M5-branes and their various configurations.

In attempting to recover elementary particles from M-theory one might attempt to study BPS-saturated solutions in supergravity theories, which are believed to survive at the full quantum level and give a glimpse of the true, non-perturbative structure of M-theory. The easiest way to find such BPS solutions is searching for extremal p-brane solitons, either in D=10,11 or in Kaluza-Klein reductions to lower dimensions. The Kaluza-Klein reductions, which include toroidal compactifications of M-theory, are especially quite nice as the procedure preserves all the original supersymmetry of the full D=11 configuration. This means, given a lower dimensional extremal BPS solution, it can be "oxidized" back up into a higher dimensional supergravity solution that preserves the same amount of supersymmetry.

The simplest extremal BPS solutions are those that preserve 1/2 of the original supersymmetry. These are solutions that contain a single charge, carried by a single field strength in supergravity. Such solutions arise in toroidally compactified M-theory down to dimensions D=3,4,5,6, and take the form of 1/2 BPS black holes.

In D=4,5,6 compactifications (M-theory on T^7, T^6 and T^5), Duff et al. noticed [2] that extremal black holes and entangled qubits share the same invariants and algebraic structures. On the M-theory side the invariants give the entropy of the black holes, while also helping to classify the various BPS solutions. On the quantum information side, the invariants help to classify the entanglement classes for qubits and qutrits. In D=3 compactifications, this black hole/qudit correspondence was even used by Levay [3] and Duff [4] to predict 9 entanglement families for four entangled qubits, where in quantum information theory the exact number has yet to be determined and predictions range from 8 to 21 families.

Recently, it has been shown [5] that by defining generalized qubits and qutrits over composition algebras (e.g., the quaternions, octonions and their split forms, etc.), it is possible to directly identify 1/2 BPS black hole solutions in D=5,6 with these generalized qubits and qutrits. This allows one to interpret qubits and qutrits (qudits) with the simplest extremal black hole solutions that contain a single charge and preserve 1/2 supersymmetry. The U-duality groups of the corresponding D=5,6 supergravity theories are then interpreted as transformations of these qudits through stochastic local operations and classical communication (SLOCC). This gives rise to new kinds of SLOCC gates in quantum information theory, which in the case of a non-associative composition algebras, endows qubits with SO(9,1), SO(5,5) symmetry and qutrits with the symmetry of the E6 exceptional Lie group.

It is quite remarkable that E6 can be interpreted as the SLOCC symmetry group of qutrits over non-associative composition algebras. Moreover, from the viewpoint of interpreting the universe as a quantum computer, it's quite desirable to have a quantum computer that processes quantum information with E6 symmetry. This is because in grand unification theories E6 is a possible gauge group which, after symmetry breaking, gives rise to the SU(3)xSU(2)xU(1) gauge group of the standard model of particle physics.

Hence, by studying BPS-saturated solutions in M-theory on T^6 (D=5, N=8 supergravity), and interpreting the simplest 1/2 BPS solutions within quantum information theory, we are inevitably led to the picture of a quantum computational theory containing qutrits with E6 symmetry. [Note: M-theory on T^6 actually has E6(6) non-compact U-duality symmetry, but upon using the full bioctonion algebra for the qutrits, compact E6(C) is recovered.] This quantum computational theory, for all practical purposes, is indistinguishable from an E6 grand unified theory, from which the standard model can be recovered. However, here, the local geometry is inherently nonassociative, as each black hole charge space, being a nonassociative C*-algebra, is associated to a spectral triple.

Ultimately, using the simplest solutions in M-theory that preserve half of their higher-dimensional supersymmetry, we arrive at a picture of the universe as a quantum computer that encodes information in the form of black holes with zero entropy. The logical operations on these black holes, as qudits, transform states within an exceptional projective space, preserving the entropy of the black holes in the process. In this picture, the ten-dimensional Lorentz group SO(9,1) and the D=5 T-duality group SO(5,5) take the form of groups of qubit transformations, which can be embedded inside E6 qutrit transformations. Thus, the dreams of Lloyd and Deutsch might eventually be realized if our universe is described by M-theory. And such a universe is computationally elegant indeed.

M-theory Computronium

2011-02-07T12:09:00.000-08:00

A fine post at the Physics and Cake blog got me thinking about computronium and how it might be realized in M-theory. Of course, this is a purely theoretical musing, but nevertheless is worthy of some consideration. For surely any advanced intelligent civilization, who have already solved M-theory will necessarily develop advanced technology that makes use of quantum gravity and its higher dimensional physics. This will especially be the case in the area of computational technology. So, using M-theory, what form might such computational technology take? Is there an M-theoretical computronium? If so, how do we program it?

Surely, the ultimate computronium is the quantum vacuum itself. Along these lines, in a string/M-theory context, by invoking the correspondence between black holes and qubits, one can see hints as to how the vacuum might eventually serve as a computational substrate. See, for example:

L. Borsten, M.J. Duff, A. Marrani, W. Rubens, On the Black-Hole/Qubit Correspondence.

In M-theory, there exist stable non-perturbative states (BPS states) with mass equal to a fraction of the supersymmetry central charge. These states arise from configurations of two and five-dimensional branes, gravitational waves and Taub-NUT-like monopoles. (Note there are no superstrings in M-theory. They arise from compactifications of M-branes in dimensional reduction from D=11 to D=10).

The black hole/qubit correspondence so far has made use of toroidal compactifications of M-theory. That is, one begins with the full 11-dimensions of M-theory and starts to curl up dimensions so that n of them form a higher-dimensional torus (doughnut shape), T^n. This then describes a lower dimensional supergravity theory, in D-n dimensions.

In the D-n dimensional supergravity theory, some BPS states arising from configurations in M-theory behave like microscopic black holes. These black holes are called extremal black holes, as they can be thought of as the ground states of black holes undergoing Hawking radiation. These states have no analog in general relativity, but do exist in supergravity and M-theory which consider quantum effects.

So far what has been found is that in M-theory compactifications down to dimensions D=3,4,5,6, BPS black hole solutions behave like entangled qubits and qutrits. More precisely, the invariants used to classify black holes with different fractions of supersymmetry, end up being the same invariants used to classify entanglement classes of qubits and qutrits. Even more, the black hole mathematical techniques classify qubits and qutrits over not only the real and complex numbers, but over higher dimensional division algebras in four and eight dimensions. So string theory actually predicts new types of qubits and qutrits and classifies their entanglement classes in advance.

Now, in practice, if M-theory is correct, the vacuum should be teeming with such microscopic black holes. They would, in a sense, serve as the qudits of an M-theoretical computronium. Specific types of transformations in M-theory called U-duality transformations, that map between BPS black hole solutions, would then serve as ‘quantum gates’ for these qudits.

Hence, to tell the M-theory vacuum what we would like to do, amounts to the programming of microscopic black holes via U-duality machine code.

Motives, Twistors and Amplitudes

2011-01-30T17:40:00.000-08:00

Nima Arkani-Hamed gave a recent talk on 01/26 entitled "Space-Time, Quantum Mechanics and Scattering Amplitudes". He essentially covers all the recent progress in the study of scattering amplitudes in dual twistor variables. He ends with hints at an underlying theory that gives rise to AdS/CFT and QFT, which might be based on the mathematical theory of motives.

For those unfamiliar the theory of motives, the goal within the mathematical community is to define a unified cohomology theory, from which all others (de Rham, Čech, singular, etc.) are special cases. It is interesting that a unified theory of physics would coincide with this platonic goal of mathematicians. Perhaps Edward Witten foresaw such a convergence and the 'M' of M-theory stood for motive all along. Either way, category theorists saw this coming a few years ago.

How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?

— Albert Einstein

Lévay on Qubits & Black Hole Horizons

2010-12-12T08:17:00.000-08:00

The BPS black hole solutions of the STU model of N=2, D=4 supergravity can be recovered from N=8, D=4 supergravity and the N=2 magic supergravities for Freudenthal triple systems in which the off-diagonal components have been diagonalized by the reduced structure group. Under D=4 U-duality, this can always be done, with the reduced structure group being in general, E6(C). Therefore, any results clarifying the quantum information interpretation of the STU model will equally apply to the N=8, D=4 and N=2 magic supergravity BPS black hole solutions. This is the case in Péter Lévay and Szilárd Szalay's November 18th pre-print: STU attractors from vanishing concurrence. The abstract is as follows:

Concurrence is an entanglement measure characterizing the mixed state bipartite correlations inside of a pure state of an n-qubit system. We show that after organizing the charges and the moduli in the STU model of N=2, d=4 supergravity to a three-qubit state, for static extremal spherically symmetric BPS black hole solutions the vanishing condition for all of the bipartite concurrences on the horizon is equivalent to the attractor equations. As a result of this the macroscopic black hole entropy given by the three-tangle can be reinterpreted as a linear entropy characterizing the pure state entanglement for an arbitrary bipartite split. Both for the BPS and non-BPS cases explicit expressions for the concurrences are obtained, with their vanishing on the horizon is demonstrated.

Atiyah on the Magic Square

2010-11-15T23:06:00.000-08:00

The Geometry and Topology of
the Freudenthal Magic Square

Sir Michael Atiyah
Edinburgh University
HKUST Institute for Advanced Study

(click images below to view videos)

The Black Hole/Qubit Correspondence

2010-10-17T21:46:00.000-07:00

The Black Hole/Qubit Correspondence
William Rubens, Imperial College

(Please be patient as video loads)

Kavli Institute for Theoretical Physics, UC Santa Barbara
Sept. 22, 2010

Feel free to leave any comments about the talk below.

Alain Connes: Fun with F1

2010-10-17T20:48:00.002-07:00

References:

Connes' Blog: NCG and F_un

Connes: On the Notion of Geometry over F_1 (PDF)

Gravity, Two Times, Six Dimensions

2010-07-12T23:34:00.000-07:00

For those interested in theories with two times, such as Itzhak Bars' S-theory, Waldron et al. have written an exciting new paper on a D=6 description of D=4 physics.

Gravity, Two Times, Tractors, Weyl Invariance and Six Dimensional Quantum Mechanics

Fefferman and Graham showed some time ago that four dimensional conformal geometries could be analyzed in terms of six dimensional, ambient, Riemannian geometries admitting a closed homothety. Recently it was shown how conformal geometry provides a description of physics manifestly invariant under local choices of unit systems. Strikingly, Einstein's equations are then equivalent to the existence of a parallel scale tractor (a six component vector subject to a certain first order covariant constancy condition at every point in four dimensional spacetime). These results suggest a six dimensional description of four dimensional physics, a viewpoint promulgated by the two times physics program of Bars. The Fefferman--Graham construction relies on a triplet of operators corresponding, respectively to a curved six dimensional light cone, the dilation generator and the Laplacian. These form an sp(2) algebra which Bars employs as a first class algebra of constraints in a six-dimensional gauge theory. In this article four dimensional gravity is recast in terms of six dimensional quantum mechanics by melding the two times and tractor approaches. This "parent" formulation of gravity is built from an infinite set of six dimensional fields. Successively integrating out these fields yields various novel descriptions of gravity including a new four dimensional one built from a scalar doublet, a tractor vector multiplet and a conformal class of metrics.

LHC Beams Collide at 7 TeV

2010-03-30T12:19:00.000-07:00

Today in Geneva Switzerland beams collided at 7 TeV in the LHC at 13:06 CEST, marking the start of the LHC research programme. Particle physicists around the world are looking forward to a potentially rich harvest of new physics as the LHC begins its first long run at an energy three and a half times higher than previously achieved at any particle accelerator.

“It’s a great day to be a particle physicist,” said CERN Director General Rolf Heuer. “A lot of people have waited a long time for this moment, but their patience and dedication is starting to pay dividends.”

“With these record-shattering collision energies, the LHC experiments are propelled into a vast region to explore, and the hunt begins for dark matter, new forces, new dimensions and the Higgs boson,” said ATLAS collaboration spokesperson, Fabiola Gianotti. “The fact that the experiments have published papers already on the basis of last year’s data bodes very well for this first physics run.”

“We’ve all been impressed with the way the LHC has performed so far,” said Guido Tonelli, spokesperson of the CMS experiment, “and it’s particularly gratifying to see how well our particle detectors are working while our physics teams worldwide are already analysing data. We’ll address soon some of the major puzzles of modern physics like the origin of mass, the grand unification of forces and the presence of abundant dark matter in the universe. I expect very exciting times in front of us.”

"This is the moment we have been waiting and preparing for", said ALICE spokesperson Jürgen Schukraft. "We're very much looking forward to the results from proton collisions, and later this year from lead-ion collisions, to give us new insights into the nature of the strong interaction and the evolution of matter in the early Universe."

“LHCb is ready for physics,” said the experiment’s spokesperson Andrei Golutvin, “we have a great research programme ahead of us exploring the nature of matter-antimatter asymmetry more profoundly than has ever been done before.”

CERN will run the LHC for 18-24 months with the objective of delivering enough data to the experiments to make significant advances across a wide range of physics channels. As soon as they have "re-discovered" the known Standard Model particles, a necessary precursor to looking for new physics, the LHC experiments will start the systematic search for the Higgs boson. With the amount of data expected, called one inverse femtobarn by physicists, the combined analysis of ATLAS and CMS will be able to explore a wide mass range, and there’s even a chance of discovery if the Higgs has a mass near 160 GeV. If it’s much lighter or very heavy, it will be harder to find in this first LHC run.

For supersymmetry, ATLAS and CMS will each have enough data to double today’s sensitivity to certain new discoveries. Experiments today are sensitive to some supersymmetric particles with masses up to 400 GeV. An inverse femtobarn at the LHC pushes the discovery range up to 800 GeV.

“The LHC has a real chance over the next two years of discovering supersymmetric particles,” explained Heuer, “and possibly giving insights into the composition of about a quarter of the Universe.”

Read More @ CERN Press

Strings 2010 - Texas A & M

2010-03-17T09:41:00.001-07:00

Strings 2010 (March 15-19) is well under way and one can view a live stream of the talks here. The schedule of talks and slides are also available. Enjoy!

Entropic Gravity

2010-02-11T17:18:00.001-08:00

On January 6th 2010, Erik Verlinde (a string theorist well known for his Matrix theory work) submitted a paper (arXiv:1001.0785) to arXiv entitled "On the Origin of Gravity and the Laws of Newton", in which he derives Newton's law of gravitation by assuming the microscopic structure of space-time is holographic. This led to a flurry of follow up papers, including notable notes by Lee Smolin (arXiv:1001.3668) and Jerzy Kowalski-Glikman (arXiv:1002.1035). In all papers, there are two basic assumptions made, from which the derivations follow. The first is a postulated microscopic holographic screen, or boundary Hilbert space, which is spherical, with surface area A=4*pi*r^2. The second is the expression for the change in entropy, which in the Jerzy Kowalki-Glikman paper arises from the entropy of a Misner string in Taub-NUT space. Any serious microscopic candidate theory for entropic gravity should be able to shed light on these two basic assumptions.

As of now, a precise microscopic theory for entropic gravity is not available, with LQG and SO(4,1) BF theory being considered as possible candidates. Ironically, the new found connection to Misner strings in Taub-NUT space makes it also probable that M-theory (suitably compactified) is the proper microscopic theory behind entropic gravity. Stay tuned.

Alien Super Earth Found

2009-12-18T00:02:00.000-08:00

Charbonneau et al. have detected a planet just six and a half times as massive as Earth - at a distance so close its atmosphere could be studied, and with a density so low it's almost certain to have abundant water.

The alien world known as GJ 1214b orbits a red dwarf star one-fifth the size of our own sun, 40 light-years away in the constellation Ophiuchus, the astronomers reported in Thursday's issue of the journal Nature.

arXiv:0912.3229v1 [astro-ph.EP]

Abstract:

A decade ago, the detection of the first transiting extrasolar planet provided a direct constraint on its composition and opened the door to spectroscopic investigations of extrasolar planetary atmospheres. As such characterization studies are feasible only for transiting systems that are both nearby and for which the planet-to-star radius ratio is relatively large, nearby small stars have been surveyed intensively. Doppler studies and microlensing have uncovered a population of planets with minimum masses of 1.9-10 times the Earth's mass (M_Earth), called super-Earths. The first constraint on the bulk composition of this novel class of planets was afforded by CoRoT-7b, but the distance and size of its star preclude atmospheric studies in the foreseeable future. Here we report observations of the transiting planet GJ 1214b, which has a mass of 6.55 M_Earth and a radius 2.68 times Earth's radius (R_Earth), indicating that it is intermediate in stature between Earth and the ice giants of the Solar System. We find that the planetary mass and radius are consistent with a composition of primarily water enshrouded by a hydrogen-helium envelope that is only 0.05% of the mass of the planet. The atmosphere is probably escaping hydrodynamically, indicating that it has undergone significant evolution during its history. As the star is small and only 13 parsecs away, the planetary atmosphere is amenable to study with current observatories.

The LHC is back!

2009-11-28T22:11:00.000-08:00

Last weekend and this week, the LHC has accomplished many tasks: it first circulated two beams in opposite directions, then made them collide in the heart of the four giant detectors and finally slightly increased their energy. Virtual champagne to the hundreds of people working nights and days to repair the machine, prepare it for new start-up and finally operate it.

Read More at CERN News

Beam of Protons Warms Up LHC

2009-10-28T17:17:00.000-07:00

(The first ion beam entering point 2 of the LHC, just before the ALICE detector October 23rd 2009)

This past weekend (October 23-25th) particles once again entered the LHC after the one-year break that followed the incident of September 2008.

Friday afternoon a first beam of ions entered the LHC's clockwise beam pipe through the TI2 transfer line. The beam was successfully guided through the ALICE detector until point 3 where it was dumped.

During the late evening on Friday, the first beam of protons also entered the LHC's clockwise ring and travelled until point 3. Saturday afternoon (October 24th), protons travelled from the SPS through the TI8 transfer line and the LHCb experiment, until point 7 where they were dumped.

All settings and parameters showed a perfect functioning of the machine, which is preparing for its first circulating beam in the coming weeks.

-CERN News

Halo Cloud Explained

2009-10-18T12:15:00.000-07:00

A strange halo cloud over Moscow had many in the Russian capital expecting a close encounter last Wednesday.

Millions witnessed an ominous ring-shaped cloud appear over Moscow’s western districts, prompting citizens to stop in their tracks to record the phenomenon and put it on YouTube.

The bizarre sight has taken the Internet by storm, so to speak.

However, scientists from the city’s weather forecast service dispelled fears of extra terrestrials landing in Red Square, saying the event was strictly environmental.

“It’s a purely optical effect, even if a spectacular one. You can see really strange things if you watch the clouds regularly,” weather officials told Russia’s Vesti 24. “Several air fronts have passed Moscow recently, including an inflow of cold air from the Arctic, and they combined to produce such a phenomenon

Indeed halo clouds have appeared elsewhere in the world, a notable example being the 'Dorset Doughnut' seen over Dorset, UK and captured in various images by the Cloud Appreciation Society.

Influence from Future in Large Hadron Collider

2009-10-13T10:55:00.000-07:00

For those that can no longer access the NYtimes article. Here is a link to the arxiv article:

Search for Effect of Influence from Future in Large Hadron Collider

We propose an experiment which consists of drawing a card and using it to decide restrictions on the running of Large Hadron Collider (LHC for short) at CERN, such as luminosity, and beam energy. There may potentially occur total shut down. The purpose of such an experiment is to search for influence from the future, that is, backward causation. Since LHC will produce particles of a mathematically new type of fundamental scalars, i.e., the Higgs particles, there is potentially a chance to find unseen effects, such as on influence going from future to past, which we suggest in the present paper.

Dark Energy and Ghost D-Branes

2009-09-26T17:07:00.000-07:00

In the recent arXiv:0906.5135, Saridakis and Ward propose a novel dark energy candidate, based on the dynamics of ghost D-branes in compactified Type II string theory. This is an approach which is based on open string dynamics that envisions a post-inflation universe living on branes that wrap cycles in the compact space, with the GUT or Electro-Weak phase transition manifested geometrically.

Ghost D-branes are defined as Dp-branes with a Z_2 symmetry that can flip the signs of the NS-NS and RR sectors (arXiv:0601024[hep-th]). By using ghost D-branes, the authors are able to recover an effective dark energy behaving either as quintessence or as a phantom field, without the need of orientifolds.

The MSSM as a Magnetic Seiberg Dual

2009-09-25T11:05:00.000-07:00

It has been known for some time that minimal SUSY SU(5) is ruled out because proton lifetimes are less than the measured limits (t_p >= 6.6 x 10^33 yrs). In arXiv:0909.4105 [hep-ph], Abel and Khoze propose that the MSSM is a magnetic Seiberg dual of an unknown electric theory. Such a proposal would explain why the supersymmetric Standard Model appears to unify but the proton does not decay. The authors put forward a number of possible dual GUTs that may provide a consistent UV completion of the minimal SU(5) model, for example with SU(11)xSp(1)^3 and SU(9)xSp(1)^3 symmetry.

Quantum Cosmological Billiards

2009-09-16T10:52:00.000-07:00

In arXiv:0907.3048, Nicolai et al. investigate cosmological singularity resolution in the context of an E_10 coset model. E_10 is the Kac-Moody big brother of E_8, the exceptional Lie group that was all the rage not long ago. The authors conclude there is a 'de-emergence' of space-time near the singularity. They also discuss observables near the singularity where they mention that the conserved E_10 Noether charges do constitute an infinite set of observables and their expectation values remain well defined in the deep quantum regime where the E_10/K(E_10) coset model is expected to replace space-time quantum field theory.

Quasiconformal Realizations of E_{6(6)}, E_{7(7)}, E_{8(8)}

2009-06-25T21:03:00.000-07:00

As mentioned at RF, Gunaydin and Pavlyk have posted a new paper arXiv:0904.0784v1 [hep-th] on non-compact exceptional groups as quasiconformal groups over the split cubic Jordan algebras. The exceptional groups E_{6(6)}, E_{7(7)}, E_{8(8)} are known to arise from toroidal compactifications of D=11 supergravity down to d dimensions, where the global non-compact symmetry group of the maximally extended supergravity is given by E_{11-d(11-d)} (arXiv:hep-th/0409263v1). It is believed the discrete subgroups E_{6(6)}(Z), E_{7(7)}(Z), E_{8(8)}(Z) yield the symmetries of the non-perturbative spectra of toroidally compactified M-theory (arXiv:hep-th/9410167v2).

Algebraically, E_{6(6)}, E_{7(7)}, E_{8(8)} arise as transformation groups of the Freudenthal triple system over the split octonions. E_{6(6)} is the subgroup of the automorphism group of the Freudenthal triple system, E_{7(7)}, which preserves the cubic form of the split exceptional Jordan algebra. Geometrically, E_{6(6)} is the collineation group of the split Moufang plane OP^2_s, the space of projectors of the split exceptional Jordan algebra. E_{7(7)} and E_{8(8)} act as conformal and quasiconformal groups, respectively, over this space.

Gunaydin and Pavlyk show in their new paper that E_{6(6)}, E_{7(7)}, E_{8(8)} individually act as quasiconformal groups over the split cubic Jordan algebras J(3,C_s), J(3,H_s) and J(3,O_s). This implies they also act as quasiconformal groups over the split projective planes CP^2_s, HP^2_s and OP^2_s, respectively. Physically, this yields a new type of duality, a duality of U-dualities, so to speak. For example, M-theory compactified on an 8-torus with D=3 U-duality group E_{6(6)} is dual to M-theory compactified on a 6-torus with D=5 U-duality group E_{6(6)} as the symmetries of the non-perturbative spectra are equivalent.

Fivebrane Structures

2009-04-13T10:10:00.000-07:00

A new jewel recently hit the arxiv: arXiv:0805.0564v3. I'll comment more about this later.

Tachyonic Inflation

2009-04-09T10:14:00.000-07:00

It is well known that inflation provides the most compelling solution to many long-standing problems of the big bang model (horizon, flatness, monopoles, etc.) The source of inflation is a scalar field (the inflaton field), which in light of modern theories, can be based on a Dirac-Borne-Infeld action rather than the conventional Klein-Gordon action, allowing the inflaton field to take the form of a tachyon field. A rolling tachyon field is usually associated with unstable D-brane configurations, where decay of such D-branes (via tachyon condensation) produces a pressureless gas with finite energy density resembling classical dust. In their April 6th paper (arXiv:0904.1032v1), del Campo et al. investigate such a tachyonic inflationary universe model in the context of intermediate inflation.

All Loop Finiteness of D=4 N=8 Supergravity?

2009-03-27T09:19:00.000-07:00

Yesterday, a striking new paper arXiv:0903.4630v1 emerged on the arxiv by the well-known Renata Kallosh. Kallosh builds on the unitary cut and pure spinor methods which have established 3-loop superfiniteness and suggested the onset of divergences starting from the 9-loop order or even all loop ﬁniteness, respectively. She specifically investigates N=8 supergravity on the light cone and makes her prediction for the actual computations using Feynman light-cone supergraphs. It is noted that light-cone superﬁeld amplitudes have a non-local structure in the transverse directions leading to the increase of the delay of divergences with the increasing number of legs in the loop-amplitudes. The delay of divergences leads to the all loop ﬁniteness prediction for N =8 supergravity.

Dyonic Giant Magnons on CP^3

2009-02-18T18:29:00.000-08:00

Kalousios et al. posted a paper (arXiv:0902.3179) today investigating a new dyonic magnon solution on CP^3. Fans of twistor theory will recall that CP^3 is actually projective twistor space. However, here the context is N=6 superconformal Chern-Simons theory with SU(N)xSU(N) symmetry, which in the large N,k limit is dual to type IIA string theory on AdS_4 x CP^3. The present paper generalizes Maldacena's giant magnon construction where it is a particular open string configuration on an R x S^2 subset of AdS_5 x S^5. This is done by noticing the equations of motion for a string on R x CP^3 are classically integrable, and supplementing them with the Virasoro constraints. Various solutions are given, such as a pointlike string moving along the equator of an S^2 in CP^3 and another on a CP^1 which is a rotation of the ordinary Hofman-Maldacena giant magnon.

Looking back at twistor string theory, Witten wanted to consider the open string B-model on CP^3, but was hindered by the fact that CP^3 is not a Calabi-Yau manifold, hence giving an anomalous R-symmetry. For this reason he considered supermanifolds of the form CP^{3|N}, which is Calabi-Yau if and only if N=4.

In the present case, type IIA string theory has no such restrictions, so it might be that Kalousios et al. have laid the foundation for a new twistor string theory on ordinary CP^3, where the perturbative expansion of the superconformal N=6 theory could be related to a D-instanton expansion of the dual string theory on AdS_4 x CP^3.

Ed Witten - Branes, Instantons, And Taub-NUT Spaces

2009-02-06T18:35:00.000-08:00

For those wondering what Ed Witten has been up to, you'll likely enjoy the new arxiv paper arXiv:0902.0948.

Blackfolds, Twistor Strings and Cosmic Strings

2009-02-04T03:38:00.000-08:00

Today's (Wed. Feb 4th) new arxiv HEP papers included some noteworthy topics, such as black holes with novel horizon geometries, N=8 twistor supergravity and cosmic superstrings. The abstracts are as follows (feel free to comment):

Blackfolds

We argue that the main feature behind novel properties of higher-dimensional black holes, compared to four-dimensional ones, is that their horizons can have two characteristic lengths of very different size. We develop a long-distance worldvolume effective theory that captures the black hole dynamics at scales much larger than the short scale. In this limit the black hole is regarded as a blackfold: a black brane (possibly boosted locally) whose worldvolume spans a curved submanifold of the spacetime. This approach reveals black objects with novel horizon geometries and topologies more complex than the black ring, but more generally it provides a new organizing framework for the dynamics of higher-dimensional black holes.

New Twistor String Theories Revisited

A gauged version of Berkovits twistor string theory featuring the particle content of N=8 supergravity was suggested by Abou-Zeid, Hull and Mason. The equations of motion for a particular multiplet in the modified theory are examined on the level of basic twistor fields and thereby shown to imply the vanishing of the negative helicity graviton on-shell. Additionally, the restrictions emerging from the equation of motion for the new gauge field \bar{B} reveal the chiral nature of interactions in theories constructed in this manner. Moreover, a particular amplitude in Berkovits open string theory is shown to be in agreement with the corresponding result in Einstein gravity.

Cosmic Strings and Cosmic Superstrings

In these lectures, I review the current status of cosmic strings and cosmic superstrings. I first discuss topological defects in the context of Grand Unified Theories, focusing in particular in cosmic strings arising as gauge theory solitons. I discuss the reconciliation between cosmic strings and cosmological inflation, I review cosmic string dynamics, cosmic string thermodynamics and cosmic string gravity, which leads to a number of interesting observational signatures. I then proceed with the notion of cosmic superstrings arising at the end of brane inflation, within the context of brane-world cosmological models inspired from string theory. I discuss the differences between cosmic superstrings and their solitonic analogues, I review our current understanding about the evolution of cosmic superstring networks, and I then briefly describe the variety of observational consequences, which may help us to get an insight into the stringy description of our Universe.

Geometry and Topology for Theoretical Physicists

2009-01-06T00:03:00.000-08:00

Happy 2009 to all U-duality readers! Today was the first day of class for the Winter term of Caltech's math sequence for theoretical physicists. This math sequence consists of three classes covering the modern mathematics a young string theorist should know. For the Fall term the main textbook was Nakahara's Geometry Topology and Physics, 2nd Edition.

This term, the main text is Morita's Geometry of Differential forms.

Today's lecture jumped right in to Čech cohomology, which can be thought of as a type of 'unifying' cohomology in the sense that it is equivalent to de Rham, simplicial and singular cohomology for well-behaved choices of topological space X. de Rham cohomology arises most frequently for physicists, but since it involves solving differential equations, it is not always the most pleasant for computations. Simplicial cohomology is probably the most computation-friendly cohomology, so Čech cohomology can be thought of as a kind of 'bridge' for translating physics problems from de Rham to a simpler (pun intended) simplicial cohomology setting. The proof of the equivalence of de Rham and Čech cohomology is most enlightening in this respect and involves forming a square of commutative (or anticommutative if you wish) mappings between vector spaces of bi-degree forms e.g. (p,q where total degree is p+q), with the vertical direction increasing via the de Rham coboundary operator, d, and horizontal direction via the Čech coboundary operator, delta. One can then define a new coboundary operator D=d+delta and show it satisfies D^2=0. I'll sketch the proof in more depth in another post, for those interested. I'll also refer the interested reader to another classic text on cohomology, namely Bott and Tu's, Differential Forms in Algebraic Topology.

Holographic Baryons

2008-12-12T00:02:00.000-08:00

Today I came across a nice talk by Shigeki Sugimoto entitled Properties of Baryons in Holographic QCD. Using Gauge/String duality, the talk explores the implications of modeling baryons as wrapped D4-branes or equivalently, instantons on D8-branes. The talk is largely based on the pre-print arXiv:0806.3122.

Status of Superstring and M-Theory

2008-12-09T10:36:00.000-08:00

A new paper, entitled "Status of Superstring and M-Theory" has recently appeared on the arxiv, written by none other than one of the fathers of string theory, John H. Schwarz. The paper is very readable and covers the history of string theory, as well as the dualities that imply the existence of an 11-dimensional M-theory underlying the various string theories and supergravity. Other topics include Flux Compactifications, Warped Compactification, Brane Worlds, String Cosmology, M-theory on G2-Manifolds and F-theory Local Models.

F-theory phenomenology (pioneered by Vafa et al) is one of the promising approaches toward connecting stringy physics to the standard model. John explains that "[t]he new proposal, which has given the subject a new lease on life, is to focus on models in which one can define a limit in which gravity is decoupled. The criterion is that it should be possible to make the dimensions transverse to the 4-cycles wrapped by the 7-branes arbitrarily large. Equivalently, it should be possible to contract the 4-cycles to points while holding the six-dimensional volume fixed. Such contractible 4-cycles must be positive curvature Kahler manifolds. These are fully classified and are given by manifolds called del Pezzo manifolds (or del Pezzo surfaces), which are denoted dP_n. The integer n takes the values 0 ≤ n ≤ 8.9 The del Pezzos have a close relationship with the exceptional Lie algebras E_n. The basic idea is that they contain 2-cycles whose intersections are characterized by the E_n Dynkin diagram. By this type of F-theory construction, one can construct an SU(5) or SO(10) SUSY-GUT model. Constructions that involve 7-branes of various types are much more subtle – and also more interesting than ones that only involve D7-branes. D7-branes are mutually local. A stack of N of them gives U(N) gauge symmetry. Matter fields at intersections (due to stretched open strings) are bifundamental. However, different kinds of 7-branes are mutually nonlocal. As a result, there are stacks (corresponding to the ADE classification of singularities) that can give U(N), SO(2N) or even E_N gauge symmetry."

So we see that F-theory, along with the use of del Pezzo surfaces enhances the usual symmetry groups one recoveres from stacks of branes. (Such symmetry groups describe the freedom the string has in choosing which brane in the stack to end on.) Phenomenologically, a configuration with E_6 symmetry would be particularly interesting.

Meteor Lights up Western Canada Skies

2008-11-22T21:17:00.000-08:00

The meteor that streaked through the darkening skies over Alberta and Saskatchewan at about 5:30 p.m. Calgary time, likely weighed between one and 10 tons and shone brightly enough to be seen over an area 700 km (435 miles) wide.

Alan Hildebrand (a planetary scientist at the University of Calgary) said the meteor may have broken into hundreds of smaller meteorites that likely landed in central Saskatchewan near that province's border with Alberta.

Black Holes, Qubits and Octonions

2008-10-13T21:22:00.000-07:00

In perhaps what is the most up-to-date paper on the quantum computation-extremal black hole-division algebra correspondence, Duff et al review all previous conjectures and suggest an alternative interpretation for which the black hole charges are identified with components of reduced density matrices. The density matrix formulation of quantum mechanics is discussed and compared to the Jordan algebraic quantum mechanics, showing the two approaches are essentially equivalent. The exceptional Jordan algebra forbids a traditional Hilbert space formulation, hence the corresponding D=5 and D=4 supergravities remain somewhat of a mystery.

LHC First beam a success

2008-09-10T09:11:00.000-07:00

Today, the first beam in the Large Hadron Collider (LHC) at CERN was successfully steered around the full 27 kilometres of the world’s most powerful particle accelerator this morning.

“It’s a fantastic moment,” said LHC project leader Lyn Evans, “we can now look forward to a new era of understanding about the origins and evolution of the universe.”

The LHC is capable of proping the energy region around 1 TeV by colliding together 7 TeV proton beams, which should reveal new physics that will address the following questions:

1) Is there a Higgs particle?

2) Is there supersymmetry (SUSY)?

3) What is dark matter?

4) Where has all the antimatter gone?

5) Why are there only six quarks?

More at press.web.cern.ch and scitech.

The LHC countdown is on!

2008-09-09T23:56:00.000-07:00

LHC First Beam on
10 September 2008

On 10 September scientists at CERN in Geneva, Switzerland will attempt for the first time to circulate a beam in the Large Hadron Collider. The LHC is the world’s most powerful particle accelerator, and will produce beams seven times more energetic, and around 30 times more intense than any previous machine when it reaches design performance.

The first injection of a beam is scheduled for 9:30 CET (+9 hours from Pacific Standard Time), and will be preceded by a planning meeting that will be relayed to the Globe from 9:00.

The Live webcast can be found here.

Edward Witten for VP?

2008-08-22T13:00:00.000-07:00

After years of work on a candidate theory of quantum gravity, there's word that the father of M-theory may well be Obama's future VP candidate. After all, it is a well-known fact that Witten was actively involved in former democratic presidential candidate George McGovern's campaign. Moreover, he has published articles in The New Republic and The Nation and has donated more than $50,000 in democratic campaign contributions from 2000-2008. Witten's desire for change clearly rivals that of any other VP hopeful. Not to mention, he's pretty darned smart. So, look out Chet Edwards and Joe Biden, your VP hopes are hanging by a string. ;)

NASA Confirms Water on Mars

2008-07-31T16:29:00.000-07:00

NASA scientists said on Thursday they had definitive proof that water exists on Mars after tests on ice found on the planet in June by the Phoenix Mars Lander.

Until now, the evidence for ice has been circumstantial. That was based on photos Phoenix took of a hard splotchy area near its landing site and changes it saw in a trench.

The robot heated up ice in one of its instruments earlier this week. Scientists say the chemical test confirms the presence of ice near the Martian north pole.

Tree Quantum Field Theory

2008-07-28T10:51:00.000-07:00

Gurau et. al. posted a new paper today on arxiv (arxiv.org/0807.4122 [hep-th]), proposing a new approach to quantum field theory: marked trees.

We propose a new formalism for quantum field theory which is neither based on functional integrals, nor on Feynman graphs, but on marked trees. This formalism is constructive, i.e. it computes correlation functions through convergent rather than divergent expansions. It applies both to Fermionic and Bosonic theories. It is compatible with the renormalization group, and it allows to define non-perturbatively {\it differential} renormalization group equations. It accommodates any general stable polynomial Lagrangian. It can equally well treat noncommutative models or matrix models such as the Grosse-Wulkenhaar model. Perhaps most importantly it removes the space-time background from its central place in QFT, paving the way for a nonperturbative definition of field theory in noninteger dimension.

SU(5) Grand Unified Model from Non-perturbative String Theory

2008-07-28T10:18:00.000-07:00

Mirjam Cvetic and Timo Weigand posted a new paper today (arXiv:0807.3953v2 [hep-th]) on symmetry breaking and SU(5) GUT model building from supergravity/non-perturbative string theory. The abstract is as follows:

We propose a robust supergravity model of dynamical supersymmetry breaking and gauge mediation, and a natural embedding in non-perturbative string theory with D-branes. A chiral field (and its mirror) charged under "anomalous" U(1)'s acts as a Polonyi field whose hierarchical Polonyi-term can be generated by string instantons. Further quartic superpotential terms arise naturally as a tree-level decoupling effect of massive string states. A robust supersymmetry breaking minimum allows for gauge mediation with soft masses at the TeV scale, which we realise for a globally consistent SU(5) GUT model of Type I string theory, with a D1-instanton inducing the Polonyi term.

Former Google Engineers Launch Cuil Search Engine

2008-07-28T10:01:00.000-07:00

A former Google employee and her husband launched a new search engine Monday called Cuil (pronounced "cool", http://www.cuil.com), aiming to topple Google by indexing more Web pages than the search giant.

Cuil, of Menlo Park, California, is led by Anna Patterson , a former leader of Google's search index and her husband, Tom Costello, who researched and developed search engines at Stanford University and IBM. The two, president and CEO, respectively, met at Stanford.

Russell Power, the third cofounder of the group, also worked at Google on search indexing, Web rankings, and spam detection. He works as vice president of engineering at Cuil.

The company, which shaved an 'L' off its name to become Cuil, said it has indexed 120 billion Web pages and can provide results organized by ideas with complete privacy for users.

Google on Friday said it had discovered 1 trillion unique Web pages on the Internet, but did not give an updated number on how many of those pages it has indexed.

Cuil said its search engine goes beyond traditional approaches by analyzing the context of each page and the concepts behind each query so it can provide better rankings by content rather than popularity. Cuil then organizes similar results into groups and sorts them by category. It also offers tabs to clarify subjects, as well as suggestions on how to refine searches.

Cuil isn't the first Google rival to launch this year. Wikia Search, a highly anticipated search engine from Wikipedia founder Jimmy Wales, made its official debut in January . Wikia Search hopes to provide better search results by allowing a community of users to index pages by using their Web page rankings and other suggestions, as well as its own indexing of the Web.

InfoWorld

The Dark Knight's Suit

2008-07-26T08:46:00.000-07:00

In "The Dark Knight," Batman complains that he needs a better suit - and that's a concern for the real-life knights in the U.S. military as well. The Pentagon would love to have Wayne Enterprises' secret for lighter, more flexible body armor. Nanocomp Technologies based in New Hampshire, is among several companies working on carbon-nanotube composites for military applications.

"We're really focused on trying to create layers of protection that would improve things for our troops," Peter Antoinette, Nanocomp's president and chief executive officer, told me. "It would take a number of years before you could order up a suit, and then a billionaire would have to pay seven figures for a suit that would work the way they do in the movies."

As an initial step, Nanocomp is working on nanotubes for next-generation wiring in satellites and aircraft. Carbon nanotubes are highly conductive and could replace copper wire in settings where reducing weight is crucial. "We're less than one-tenth the weight of copper, so if you can take 1,000 pounds off these satellites or aircraft, you'd be saving a huge amount of money," Antoinette said.

Commercialization of nanotube wiring could begin as early as next year, Antoinette said. He added that Nanocomp's materials are already undergoing military testing, and body-armor applications could start emerging in 2010 or so.

Kakalios agreed that nanotubes are a technology to watch: "Compared to steel cables, it's about 100 times stronger. Whether you can make this in large enough quantities, in long enough length scales ... that work is still in progress."

CosmicLog

Northern Lights Explained

2008-07-26T08:27:00.000-07:00

NASA released findings Thursday that indicate magnetic explosions about one-third of the way to the moon cause the northern lights, or aurora borealis, to dance across the sky in spectacular shapes and colors.

A fleet of five small satellites, called Themis, observed the beginning of a geomagnetic storm in February, while ground observatories recorded the brightening of the northern lights.

A team led by UCLA scientist Vassilis Angelopoulos confirmed that the observed storm about 80,000 miles from Earth was triggered by a phenomenon known as magnetic reconnection. Every so often, the Earth's magnetic field lines are stretched like rubber bands by solar energy, snap, are thrown back to Earth and reconnect, in effect creating a short circuit.

This stored-up energy powers the northern and southern lights, Angelopoulos said.

LA Times

Xian-Jin Li and an attempted Proof of the Riemann Hypothesis

2008-07-04T08:23:00.000-07:00

A new paper by Xian-Jin Li was uploaded on arxiv this week, with a claimed "proof" of the Riemann Hypothesis. Well, a "proof" is actually given for E. Bombieri's refinement of A. Weil's positivity condition, which implies the Riemann Hypothesis. The "proof" is said to be in the spirit of Alain Connes' approach to the Riemann Hypothesis.

Fortunately, (or unfortunately) it didn't take too long for Fields medalists to punch holes in the purported proof. Alain Connes himself, as well as Terence Tao pointed out certain problems on pages 20 and 29.

Alain Connes politely states in his blog:

I dont like to be too negative in my comments. Li's paper is an attempt to prove a variant of the global trace formula of my paper in Selecta. The "proof" is that of Theorem 7.3 page 29 in Li's paper, but I stopped reading it when I saw that he is extending the test function h from ideles to adeles by 0 outside ideles and then using Fourier transform (see page 31). This cannot work and ideles form a set of measure 0 inside adeles (unlike what happens when one only deals with finitely many places).

While Terence Tao, adds:

It unfortunately seems that the decomposition claimed in equation (6.9) on page 20 of that paper is, in fact, impossible; it would endow the function h (which is holding the arithmetical information about the primes) with an extremely strong dilation symmetry which it does not actually obey. It seems that the author was relying on this symmetry to make the adelic Fourier transform far more powerful than it really ought to be for this problem.

Xian-Jin Li has since posted revisions of his paper, specifically making changes on page 20 and 29, where Connes and Tao pointed out difficulties. However, it is doubtful Connes and Tao will take another look at the new version of the paper.

Extremal Black Holes & Elementary Particles (1995)

2008-04-06T02:33:00.000-07:00

Witten and Seiberg found a way to eliminate certain singularities in a four-dimensional quantum field theory with supersymmetry--an extension of the standard model of particle physics that attempts to incorporate all the forces of nature except gravity. They did it by introducing to the theory a hypothetical particle called a magnetic monopole.

By gradually changing a particular parameter in the equations describing supersymmetry, the theorists could show that this monopole becomes massless right when the equations, in the absence of monopoles, point to infinity as the answer. This approach makes it possible to circumvent troubling singularities and obtain reasonable solutions to the equations.

Strominger asked himself whether miniature black holes carrying an electric charge might play a similar role in string theory. These curious objects are closely related to the black holes of relativity theory and astronomical speculation.

"Ordinary" astronomical black holes are generally characterized by their mass, electric charge, and angular momentum, or spin. In string theory, researchers deal with "extremal" black holes--tiny bodies with mass and charge comparable to those of elementary particles.

Strominger looked at what happens to such a black hole when one varies parameters determining the shapes of the curled-up, six-dimensional spaces that arise in string theory. He discovered that as the shape changes, the mass of a charged black hole dwindles to zero precisely when the singularities he was worried about would arise.

At first glance, the notion of a massless black hole may seem contradictory, but it arises naturally out of the mechanics of string theory. In some situations, a black hole's mass is proportional to its area. Making this area smaller and smaller eventually leads to a black hole with zero mass.

"It's a very special kind of black hole," Greene says. "But it's still sensible to think of it as being a black hole, because it evolved from a massive black hole."

The transformations studied by Strominger also revealed a direct correspondence between extremal black holes and strings. He could avoid the singularities normally encountered in the particular formulation of string theory he was using by treating black holes as strings and strings as black holes.

When Greene and Morrison heard about Strominger's work, they quickly realized there was no barrier to continuing a shape transformation beyond the massless black hole stage. In fact, this stage appeared to mark a transition not unlike that occurring when a solid melts or a liquid freezes.

In the case of water, for example, lowering the temperature turns the liquid to ice. Raising the temperature reverses the process. Although ice and liquid water look and behave differently, they merely represent two phases of the same molecular substance.

Something similar happens as the geometry of the six-dimensional components of string theory gradually changes. At a certain critical value of a shape parameter, one gets a phase transition in which tiny, charged black holes are transformed into strings in specific vibrational states. The vibrating strings, in turn, correspond to various elementary particles.

"When you follow the transition in detail, what appear to be black holes in the first phase--analogous to water--evolve into fundamental particles in the second phase--analogous to ice," Greene says. "That is, black holes reappear as more conventional elementary particles, such as electrons or quarks."

"What wasn't clear, but becomes obvious with this work, is that black holes and elementary particles are really one and the same thing as they smoothly change from one to another," he adds.

The researchers also noted that, at the same moment black holes transmute into elementary particle states, the topology, or basic geometric shape, of the accompanying six-dimensional space changes markedly. Such topological transformations can be as radical as changing a beach ball into a doughnut-shaped ring by ripping a hole in the plastic before reshaping the material into its new form.

Science News, August 26, 1995 by Ivars Peterson

SUSY Bet @ Burning Man

2008-02-26T10:28:00.000-08:00

Here's a video I came across of some physics students and Garret Lisi talking SUSY physics at Burning Man, August 30, 2006. Apparently Garret is betting that SUSY particles will not be found at the LHC by 2010. Either way, I enjoy the physics discussion amidst the echoing electronic music. Perhaps Garret should schedule a quantum gravity mini-seminar at Burning Man 2010 and invite physics and math PhD students from around the world!

Antimatter from X-ray binary stars

2008-01-16T10:58:00.000-08:00

In 1978, gamma ray detectors flown on balloons detected a type of gamma ray emerging from space that is known to be emitted when electrons collide with positrons — meaning there was antimatter in space.

"It was quite a surprise back then to discover part of the universe was made of antimatter," researcher Gerry Skinner, an astrophysicist at Goddard Space Flight Center in Greenbelt, Md., told SPACE.com.

These gamma rays apparently came from a cloud of antimatter roughly 10,000 light-years across surrounding our galaxy's core. This giant cloud shines brightly with gamma rays, with about the energy of 10,000 suns.

What exactly generated the antimatter was a mystery for the following decades. Suspects have included everything from exploding stars to dark matter.

Now, an international research team looking over four years of data from the European Space Agency's International Gamma Ray Astrophysics Laboratory (INTEGRAL) satellite has pinpointed the apparent culprits. Their new findings suggest these positrons originate mainly from stars getting devoured by black holes and neutron stars.

The researchers calculate that a relatively ordinary star getting torn apart by a black hole or neutron star orbiting around it — a so-called "low mass X-ray binary" — could spew on the order of one hundred thousand billion billion billion billion positrons (a 1 followed by 41 zeroes) per second. These could account for a great deal of the antimatter that scientists have inferred, reducing or potentially eliminating the need for exotic explanations such as ones involving dark matter.

"Simple estimates suggest that about half and possibly all the antimatter is coming from X-ray binaries," said researcher Georg Weidenspointner of the Max Planck Institute for Extraterrestrial Physics in Germany.

Now that they have witnessed the death of antimatter, the scientists hope to see its birth.

"It would be interesting if black holes produced more matter than neutron stars, or vice versa, although it's too early to say one way or the other right now," Skinner explained. "It can be surprisingly hard to tell the difference between an X-ray binaries that hold black holes and neutron stars."

E11 and M-theory

2007-11-26T08:44:00.001-08:00

One of the recent jewels to arrive in hep-th is Paul Cook's Connections between Kac-Moody algebras and M-theory. This paper is actually a PhD thesis, under the supervision Peter West, the author of the well-known Introduction to Supersymmetry and Supergravity text.

By now, most people on the blogosphere have heard of the 248-dimensional Lie group E8. However, E8 isn't really "big" enough for M-theory. To capture the robust objects found in M-theory Cook argues one must use E8's Kac-Moody brother E11, i.e., that the Kac-Moody algebra E11 encodes the symmetries of M-theory.

As evidence for his conjecture, Cook finds the closure of a group G11 (an enlargement of the affine group IGL(11)) which includes two generators whose associated gauge fields are those of the only branes found in M-theory: the M2 and M5 branes. This essentially leads to a nonlinear realization of 11D-supergravity, where it is argued that a hidden E8 symmetry is manifest before the usual compactification to the three dimensions.

Garrett Lisi's Theory of Everything

2007-11-16T02:49:00.000-08:00

Garret Lisi's "Exceptionally Simple Theory of Everything" has been all the rage lately, being a hot topic of discussion at all the major physics blogs and even landing a front page article at New Scientist. Garrett's theory uses a non-compact form of E8, which supergravity buffs might recognize as a quasiconformal group for extremal black holes in homogeneous supergraviy. For the non-supergravity buffs this means the non-compact forms of E8 act as symmetry groups of the 57-dimensional charge-entropy space of microscopic black holes. This is the same 57-dimensional object mentioned in the E8 computation earlier this year.

From a quick listen of Garrett's talk at LSU, it seems the loop quantum gravity community finds Garrett's ideas to be promising. In the audio version of the talk, Smolin and Ashtekar can be heard commenting on a possible spin-network version of Garrett's model. Only time will tell if there is a spin-network/spin-foam formulation of Garrett's model. I, on the other hand, see more similarities with supergravity; and if this relation is real, there might actually be a topological string theory behind Garrett's TOE. D'oh! ;)

Whatever Happened to Twistor Strings?

2007-10-08T21:46:00.000-07:00

For those of you wondering if twistor strings vanished into obscurity, I found some recent arxiv papers on the subject. There was an august phenomenology paper on the twistor string entitled A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes.

The abstract is as follows:

Recent progress in unitarity techniques for one-loop scattering amplitudes makes a numerical implementation of this method possible. We present a 4-dimensional unitarity method for calculating the cut-constructible part of amplitudes and implement the method in a numerical procedure. Our technique can be applied to any one-loop scattering amplitude and offers the possibility that one-loop calculations can be performed in an automatic fashion, as tree-level amplitudes are currently done. Instead of individual Feynman diagrams, the ingredients for our one-loop evaluation are tree-level amplitudes, which are often already known. To study the practicality of this method we evaluate the cut-constructible part of the 4, 5 and 6 gluon one-loop amplitudes numerically, using the analytically known 4, 5 and 6 gluon tree-level amplitudes. Comparisons with analytic answers are performed to ascertain the numerical accuracy of the method.

Others which deserve honorable mention are Twistor Strings with Flavour and Balanced Superprojective Varieties. I especially have to find the time to digest the latter, as the notion of a superprojective space as a functor-of-points seems useful.

A Forthcoming Change of Signature?

2007-10-05T11:22:00.000-07:00

Mars et al. make compelling arguments in gr-qc: 0710.0820 that the Universe's accelerated approach towards a future singularity may be due to a change in signature of our braneworld in a bulk 5D Anti de Sitter space (AdS_5).

The authors argue that by choosing hypersurfaces in AdS_5 appropriately, it is possible to construct signature changing branes, with well behaved properties. They explain that hypothetical scientists living on such a hypersurface in AdS_5 might not realize that they are living on a brane, much less a brane that can undergo a Lorentzian -> Euclidean signature change. If the scientists living on the brane use General Relativity as their gravitational theory, they will find that the eigenvalues of the brane Einstein tensor diverge at a 'singularity' placed on the signature changing set. This type of singularity has recently been called a sudden singularity, as well as 'type III' singularity and 'big freeze'. Sudden singularities violate certain energy conditions, signaling the existence of phantom or dark energy components, an illusion caused by an imminent signature change on the brane.

The paper is a nice 8-page read for anyone interested in braneworld cosmology.

Hawking Radiation from Extremal and Non-Extremal Black Holes

2007-10-03T16:06:00.001-07:00

The relationship between extremal and non-extremal black holes was recently studied by Balbinot et al. in hep-th: 0710.0388. As readers of this blog know, extremal black holes have been all the rage in the string theory community. This is because using D-brane techniques, it is possible to construct an extremal black hole and calculate its entropy. That such D-brane approaches yield an entropy that agrees with the Bekenstein-Hawking formula was hailed as a major triumph for string theory. More recently, Gunaydin and Ferrara have shown that the entropy of black holes in magic supergravities can be calculated using cubic and quartic invariants of the so-called U-duality groups.

Given such success in finding the entropy of extremal black holes, one might wonder why there wasn't more buzz in the popular media. A likely reason is that extremal black holes are rather exotic types of black holes. They have a mass that equals their charge, and are very much unlike the large black holes that astrophysicists rave about. What Balbinot et al. show in their paper is how to continuously transform a non-extremal black hole to an extremal black hole in the limit that mass approaches charge. This was thought to be impossible, as there were arguments that the non-extremal and extremal black holes are distinct quantum mechanical objects.

The arguments in the Balbinot paper are based on a two-dimensional analytical treatment, but the authors argue that their techniques generalize to the four-dimensional case.

M-Theory Through the Looking Glass

2007-09-24T18:30:00.000-07:00

A new paper by Horava and Keeler came out a few days ago, with the whimsical title M-Theory Through the Looking Glass: Tachyon Condensation in the E_8 Heterotic String. Luboš Motl gave it a thumbs up, as do I for the use of only one copy of E8. The abstract is as follows:

We study the spacetime decay to nothing in string theory and M-theory. First we recall a nonsupersymmetric version of heterotic M-theory, in which bubbles of nothing -- connecting the two E_8 boundaries by a throat -- are expected to be nucleated. We argue that the fate of this system should be addressed at weak string coupling, where the nonperturbative instanton instability is expected to turn into a perturbative tachyonic one. We identify the unique string theory that could describe this process: The heterotic model with one E_8 gauge group and a singlet tachyon. We then use worldsheet methods to study the tachyon condensation in the NSR formulation of this model, and show that it induces a worldsheet super-Higgs effect. The main theme of our analysis is the possibility of making meaningful alternative gauge choices for worldsheet supersymmetry, in place of the conventional superconformal gauge. We show in a version of unitary gauge how the worldsheet gravitino assimilates the goldstino and becomes dynamical. This picture clarifies recent results of Hellerman and Swanson. We also present analogs of R_\xi gauges, and note the importance of logarithmic CFT in the context of tachyon condensation.

The Flying Car

2007-09-01T20:13:00.000-07:00

Tired of being stuck in traffic?

According to the Moller website, the Skycar sits four passengers, has a maximum speed of 375 MPH, runs on ethanol (yes, ethanol Carl!) and best of all has a low-end price tag of only $500,000. ;)

Topology change and new phases of N=4 SYM theory

2007-06-04T21:35:00.000-07:00

Last friday (06/01/07), I attended the last of the Winter 2007 Caltech High Energy Seminars. The talk was at 1pm, given by KITP post-doc Sean Hartnoll. Hartnoll discussed topological phase changes of N=4 SYM theory (hep-th/0703100). Using both numerical and analytical techniques, Hartnoll found that at weak coupling, the six-sphere eigenvalue distribution transitions to a five-sphere distribution.

An interesting interpretation of this second order phase transition involves the fate of the large AdS black hole spacetime at weak coupling. Given that there are no further phase transitions as a function of coupling, the AdS black hole is described by the five-sphere eigenvalue distribution.

Hartnoll also explained how the five-sphere distribution generalizes the two-dimensional quantum Hall effect. During the question and answer session I mentioned the four and eight-dimensional quantum Hall effects to Hartnoll. He agreed that it would be interesting if his techniques could be applied in such dimensions.

Mapping the geometry of the F4 group

2007-05-29T19:19:00.000-07:00

While browsing the arxiv, I came upon a cool new paper on the group F4. The paper contains a plethora of mathematical treasures, including: the exceptional Jordan algebra, OP^2 and the generalized F4 Euler angle construction I mentioned to Kea and Carl earlier this year. Pierre Ramond explored these issues in the context of M-theory back in 1998 (hep-th/9808190). More recently, the physical context has been extended to extremal black holes in N=2 Maxwell-Einstein supergravities (hep-th/0512296).

Mapping the geometry of the F4 group

Abstract:

In this paper we present a construction of the compact form of the exceptional Lie group F4 by exponentiating the corresponding Lie algebra f4. We realize F4 as the automorphisms group of the exceptional Jordan algebra, whose elements are 3 x 3 hermitian matrices with octonionic entries. We use a parametrization which generalizes the Euler angles for SU(2) and is based on the fibration of F4 via a Spin(9) subgroup as a fiber. This technique allows us to determine an explicit expression for the Haar invariant measure on the F4 group manifold. Apart from shedding light on the structure of F4 and its coset manifold OP2=F4/Spin(9), the octonionic projective plane, these results are a prerequisite for the study of E6, of which F4 is a (maximal) subgroup.

Strings in Two Minutes or Less

2007-05-01T11:18:00.000-07:00

The eight finalists for the Discover Magazine "String Theory in Two Minutes of Less" contest have been selected and can be found at discovermagazine.com. Even though Brian Greene is the official contest judge, there is a viewer's choice award that net surfers can participate in. I casted my vote for the 'String Ducky' entry, as it is pretty accurate and easy to follow. Which is your choice?

Hawking in Space

2007-04-26T15:48:00.000-07:00

Already a giant in theoretical physics, Stephen Hawking has just completed eight rounds of zero-G weightlessness in preparation for his journey into space. The zero-G flight took place on a modified Boeing 727 plane named "G-Force One", boarded at NASA's Shuttle Landing Facility in Florida. As to why Hawking is going through so much trouble for space flight, he commented:

"Many people have asked me why I am taking this flight. I am doing it for many reasons. First of all, I believe that life on earth is at an ever-increasing risk of being wiped out by a disaster such as sudden global warming, nuclear war, a genetically engineered virus or other danger. I think the human race has no future if it doesn’t go into space. I therefore want to encourage public interest in space.

"I have long wanted to go into space, and the zero-gravity flight is the first step toward space travel. I also want to demonstrate to the public that everyone can participate in this type of weightless experience.

"Finally, I am doing this flight to raise money for a number of charities, including ALS, Easter Seals, Starlight Starbright and the X Prize Foundation."

The planned space trip has been so inspiring that Steve Kohler, president of Space Florida, has renamed the zero-gravity research center in Hawking's honor.

Full Cosmic Log (MSNBC) ...

(photo by Steve Boxall)

E6 and Entanglement of Three Qutrits

2007-04-12T09:52:00.000-07:00

Michael Duff and Sergio Ferrara posted a follow-up to their papers Black hole entropy and quantum information and E_7 and the tripartite entanglement of seven qubits entitled E_6 and the bipartite entanglement of three qutrits. In order to relate quantum information to 5D black holes, they invoked the use of qutrits, the ternary logic generalizations of qubits. This is a very natural choice and has its roots in the structure of Jordan algebras of degree three. Jordan algebras of degree three underlie the N=2 5D magical supergravities where the charge space of N=2 5D BPS black holes is equated with the Jordan algebra as a vector space over R. In the octonionic case, the Jordan algebra of degree three is called the exceptional Jordan algebra, and the black hole charge space has real dimension 27.

At the end of the paper, Duff and Ferrara state that the "analogy between black holes and quantum information remains, for the moment, just that" and that they "know of no physics connecting them." They mention a comment by Murat Gunaydin (via private communication) suggesting that "the appearance of octonions and split-octonions implies a connection to quaternionic and/or octonionic quantum mechanics." Murat's comment seem quite accurate, but the details of the quaternionic/octonionic quantum mechanics are quite subtle. In 1934, Pascual Jordan, John von Neumann and Eugene Wigner investigated quaternionic/octonionic quantum mechanics and found problems in their Hilbert space formulations. Bischoff in 1993, eventually gave a Hilbert space formulation using the regular representation of the Jordan algebras of degree three. Support for this approach was given by Dray and Manogue's Exceptional Jordan eigenvalue problem. My most recent paper combines the work of Bischoff, Dray and Manogue and elucidates the role of eigenmatrices in the description of N=2 extremal black holes with symmetric moduli space E6(-26)/F4.

The interplay between extremal black holes, entangled qutrits and octonionic quantum mechanics is quite elegant. I tend to take the view that quantum information is the most fundamental, however. Jordan algebras, Freudenthal triple systems and octonions may ultimately be just convenient representations for the description of the quantum logic of nature. As the year progresses, we'll see how this story unfolds, and if we're lucky it will reveal secrets about the nature of spacetime itself.

Jordan Algebras and Extremal Black Holes

2007-03-28T18:05:00.000-07:00

Back in 2003, Pierre Ramond wrote a classic paper entitled Exceptional Groups and Physics where he considered the mysterious relationship between M-theory and the exceptional Lie groups. On pages 8 and 9, he discussed the exceptional Jordan algebra (EJA) and its automorphism group F4, arguing that the SO(9) subgroup of F4 should be interpreted as the light-cone little group in eleven dimensions. He concluded with the statement:

"If the SO(9) subgroup of [the] EJA automorphism group F4 can indeed be identified with the light-cone little group in eleven space-time dimensions, it will suggest the EJA as the charge space of a very special system."

In February 2005, Murat Gunaydin showed the EJA is actually the charge space of an extremal black hole in N=2, d=5 Maxwell-Einstein supergravity. Come summer 2005, Andrew Neitzke, Boris Pioline and Andrew Waldron joined forces with Murat Gunaydin and formulated a method for counting microstates of four-dimensional BPS black holes in N >= 2 Maxwell-Einstein supergravities. Gunaydin gave a December 9th talk on the approach at the KITP and by December 22 the work culminated in a paper entitled BPS black holes, quantum attractor flows and automorphic forms.

It turns out there are more Jordan algebraic goodies that add to the story, so I put together a paper and posted it here. :)

(Note: The image above is a depiction of the Bajoran wormhole from the Star Trek: Deep Space Nine series)

Ternary Logic

2007-03-22T21:32:00.000-07:00

Earlier this week, Kyle (a fellow physics grad student) got me thinking about the set of single variable functions from a finite set A={a,b,c} to a finite set B={0,1,2}. Such functions involve triples of elements of A x B, and take for example the form f_012={(a,0), (b,1), (c,2)}. I ended up using shorthand for such functions, writing f_012 as 012 for instance, to reveal the nice single variable ternary function structure. Ultimately, I came up with the above diagram to show how multiple copies of the parity cube vertices arise in this set of functions. I guess one can also look at it as a Qutrit function diagram. Kea and Carl may see further applications in particle physics. ;)

AIM Team Maps E8

2007-03-19T16:25:00.000-07:00

Congratulations to the Atlas team for their fine work in computing the Kazhdan-Lusztig-Vogan polynomials for the large block of the split real form of E₈. AIM's popular overview can be found on their E8 page. For the wonderful details see the Atlas overview.

3D Discrete Dynamical Systems

2007-03-16T11:29:00.000-07:00

Shown above are 3D scatter plots of several trajectories for a saddle point origin. The program is written in C, based on an old computer graphics project. The L triplet denotes the eigenvalues used to generate the system.

Standard Model Particle Masses

2007-03-11T15:59:00.000-07:00

For all of you that suddenly awaken at night (in a cold sweat) because you forgot your SM particle masses, make sure to check out the PDG page for a refresher.

Twistors' Revenge

2007-01-25T12:16:00.000-08:00

One of the recent (Jan 23) jewels on the arxiv is Andrew Neitzke, Boris Pioline and Stefan Vandoren's "Twistors and Black Holes" paper. It seems quaternionic-Kahler manifolds are all the rage now.

Twistors and Black Holes

Abstract:
"Motivated by black hole physics in N=2, D=4 supergravity, we study the geometry of quaternionic-Kahler manifolds M obtained by the c-map construction from projective special Kahler manifolds M_s. Improving on earlier treatments, we compute the Kahler potentials on the twistor space Z and Swann space S in the complex coordinates adapted to the Heisenberg symmetries. The results bear a simple relation to the Hesse potential \Sigma of the special Kahler manifold M_s, and hence to the Bekenstein-Hawking entropy for BPS black holes. We explicitly construct the ``covariant c-map'' and the ``twistor map'', which relate real coordinates on M x CP^1 (resp. M x R^4/Z_2) to complex coordinates on Z (resp. S). As applications, we solve for the general BPS geodesic motion on M, and provide explicit integral formulae for the quaternionic Penrose transform relating elements of H^1(Z,O(-k)) to massless fields on M annihilated by first or second order differential operators. Finally, we compute the exact radial wave function (in the supergravity approximation) for BPS black holes with fixed electric and magnetic charges."

NASA Announces Dark Matter Discovery

2006-08-20T17:30:00.000-07:00

Astronomers will announce how dark and normal matter have been forced apart in an extraordinarily energetic collision at 1 p.m. EDT Monday, Aug. 21.