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## Tuesday, December 09, 2008

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Status of Superstring and M-Theory

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.

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.

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## 1 comment:

Hi Kneemo,

Thanks for this reference.

I notice that Schwartz did not provide a definition for U-duality in section 2.2.5 on page 8 as he did for T- and S-duality.

The word dynamics seems to appear more and more often in this literature. I find this intriguing.

Themophysicists at the Russian Academy of Sciences are using mathematical dynamics. I recommenend reading this Springer book which can be searched on Amazon:

SV Alekseenko, PA Kuibin, VL Okulov,

Theory of Concentrated Vortices: An Introduction.

Vortices are spin vectors relating to solenoids ususally helical but can be toroidal. The authors use the Biot-Savard law from electromagnetism in this perturbative theory.

The authors discuss 'helical filaments' within Beltrami flows. From my perspective these filaments are descriptions of strings in this type of dynamics.

The book deals primarily with fluid flows, but does allude to the use of this theory in plasma physics, dynamos and magnetohydrodynamics. There are books on the physiology of blood flows that appear related.

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