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! ;)
Agreed!! I'm glad you posted about this, and I'm really surprised that you're the only string theorist so far to have said something positive about the Lisi paper. I look forward to further posts.
I was under the impression that E8 is a torus. I can see elements of this in the Lisi animation, but there also appear to be non-torus elements.
"The Weyl group of E8, which acts as a symmetry group of the maximal torus by means of the conjugation operation from the whole group, is of order 696729600." and "E8 is the U-duality group of supergravity on an eight-torus (in its split form)." http://en.wikipedia.org/wiki/E8_(mathematics)
Evslin, Jarah, ‘From E8 to F via T' Abstract: We argue that T-duality and F-theory appear automatically in the E8 gauge bundle perspective of M-theory. The 11-dimensional supergravity four-form determines an E8 bundle. If we compactify on a two-torus, this data specifies an LLE8 bundle where LG is a centrally-extended loopgroup of G. If one of the circles of the torus is smaller than surd(alpha') then it is also smaller than a nontrivial circle S in the LLE8 fiber and so a dimensional reduction on the total space of the bundle is not valid. We conjecture that S is the circle on which the T-dual type IIB theory is compactified, with the aforementioned torus playing the role of the F-theory torus. As tests we reproduce the T-dualities between NS5-branes and KK-monopoles, as well as D6 and D7-branes where we find the desired F-theory monodromy. Using Hull's proposal for massive IIA, this realization of T-duality allows us to confirm that the Romans mass is the central extension of our LE8. In addition this construction immediately reproduces the conjectured formula for global topology change from T-duality with H-flux. http://adsabs.harvard.edu/abs/2004JHEP...08..021E
There is also this illustration [1 Tokamak Basics] of a torus-helix relation at Physics World, Richard Pitts, Richard Buttery, Simon Pinches, 'Fusion: the way ahead', 1 Mar 2006. [Not E8 specifically, but one of my preferred visualizations of E8] http://physicsworld.com/cws/article/print/24295/1/PWfus3_03-06
11-dimensional supergravity is the effective low energy theory of strongly coupled M-theory. When you compactify 7 of the 11-dimensions on a torus, you get a maximally extended supergravity with global non-compact symmetry group E8(8).
The other non-compact real form of E8, namely E8(-24), doesn't have such a straightforward relation to M-theory and is still a work in progress. For now, E8(-24) is known to be a symmetry group for homogeneous supergravity in 3 dimensions. Evidence suggests that such a supergravity arises from a topological string theory.
I think the introduction to the paper gives it away already:
"We exist in a universe described by mathematics" ....... "The mathematics of the universe should be beautiful".
This seems to be just another case of mathematical mysticism and should not qualify as rational science (even it appears to reproduce certain aspects of reality). The scheme suggested reminds me vaguely of astrological models and Kepler's attempt to explain the solar system in terms of regular polyhedra (see http://www.hps.cam.ac.uk/starry/keplerastrol.html, http://hyperion.cc.uregina.ca/~astro/Kepler_poly.html ) and we all know what the scientific status of this is nowadays.
Mathematics should be a tool, not an end in itself.
5 comments:
Agreed!! I'm glad you posted about this, and I'm really surprised that you're the only string theorist so far to have said something positive about the Lisi paper. I look forward to further posts.
Y'all might try my new rotation applet of the E8 roots I typed up last night.
The base code was the stuff I wrote for Kea's Fourier transform things. I wanted to get nice patterns from the baryons, but I still haven't got them.
Hi Kneemo,
I was under the impression that E8 is a torus. I can see elements of this in the Lisi animation, but there also appear to be non-torus elements.
"The Weyl group of E8, which acts as a symmetry group of the maximal torus by means of the conjugation operation from the whole group, is of order 696729600."
and
"E8 is the U-duality group of supergravity on an eight-torus (in its split form)."
http://en.wikipedia.org/wiki/E8_(mathematics)
Evslin, Jarah, ‘From E8 to F via T'
Abstract: We argue that T-duality and F-theory appear automatically in the E8 gauge bundle perspective of M-theory. The 11-dimensional supergravity four-form determines an E8 bundle. If we compactify on a two-torus, this data specifies an LLE8 bundle where LG is a centrally-extended loopgroup of G. If one of the circles of the torus is smaller than surd(alpha') then it is also smaller than a nontrivial circle S in the LLE8 fiber and so a dimensional reduction on the total space of the bundle is not valid. We conjecture that S is the circle on which the T-dual type IIB theory is compactified, with the aforementioned torus playing the role of the F-theory torus. As tests we reproduce the T-dualities between NS5-branes and KK-monopoles, as well as D6 and D7-branes where we find the desired F-theory monodromy. Using Hull's proposal for massive IIA, this realization of T-duality allows us to confirm that the Romans mass is the central extension of our LE8. In addition this construction immediately reproduces the conjectured formula for global topology change from T-duality with H-flux.
http://adsabs.harvard.edu/abs/2004JHEP...08..021E
There is also this illustration [1 Tokamak Basics] of a torus-helix relation at Physics World, Richard Pitts, Richard Buttery, Simon Pinches, 'Fusion: the way ahead', 1 Mar 2006. [Not E8 specifically, but one of my preferred visualizations of E8]
http://physicsworld.com/cws/article/print/24295/1/PWfus3_03-06
Hi Doug
11-dimensional supergravity is the effective low energy theory of strongly coupled M-theory. When you compactify 7 of the 11-dimensions on a torus, you get a maximally extended supergravity with global non-compact symmetry group E8(8).
The other non-compact real form of E8, namely E8(-24), doesn't have such a straightforward relation to M-theory and is still a work in progress. For now, E8(-24) is known to be a symmetry group for homogeneous supergravity in 3 dimensions. Evidence suggests that such a supergravity arises from a topological string theory.
I think the introduction to the paper gives it away already:
"We exist in a universe described by mathematics" ....... "The mathematics of the universe should be beautiful".
This seems to be just another case of mathematical mysticism and should not qualify as rational science (even it appears to reproduce certain aspects of reality). The scheme suggested reminds me vaguely of astrological models and Kepler's attempt to explain the solar system in terms of regular polyhedra (see http://www.hps.cam.ac.uk/starry/keplerastrol.html, http://hyperion.cc.uregina.ca/~astro/Kepler_poly.html ) and we all know what the scientific status of this is nowadays.
Mathematics should be a tool, not an end in itself.
Thomas
http://www.physicsmyths.org.uk
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