http://inspirehep.net/record/499969/files/arXiv:hep-th_9905111.pdf

Large N Field Theories, String Theory and Gravity

We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero B-field. We identify a limit in which the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a noncommutative space, and discuss the corrections away from this limit. Our analysis leads us to an equivalence between ordinary gauge fields and noncommutative gauge fields, which is realized by a change of variables that can be described explicitly. This change of variables is checked by comparing the ordinary Dirac-Born-Infeld theory with its noncommutative counterpart. We obtain a new perspective on noncommutative gauge theory on a torus, its T-duality, and Morita equivalence. We also discuss the D0/D4 system, the relation to M-theory in DLCQ, and a possible noncommutative version of the six-dimensional (2,0) theory.

https://iopscience.iop.org/article/10.1088/1126-6708/1999/09/032/pdf

String theory and noncommutative geometry

The correspondence between supergravity (and string theory) on AdS space and boundary conformal eld theory relates the thermodynamics of N = 4 super Yang-Mills theory in four dimensions to the thermodynamics of Schwarzschild black holes in Anti-de Sitter space. In this description, quantum phenomena such as the spontaneous breaking of the center of the gauge group, magnetic connement, and the mass gap are coded in classical geometry. The correspondence makes it manifest that the entropy of a very large AdS Schwarzschild black hole must scale \holographically" with the volume of its horizon. By similar methods, one can also make a speculative proposal for the description of large N gauge theories in four dimensions without supersymmetry.

https://www.intlpress.com/site/pub/files/_fulltext/journals/atmp/1998/0002/0003/ATMP-1998-0002-0003-a003.pdf

Anti-de Sitter Space, Thermal Phase Transition, And Confinement in Gauge Theories

We suggest and motivate a precise equivalence between uncompactified 11-dimensional $M$ theory and the $N=\ensuremath{\infty}$ limit of the supersymmetric matrix quantum mechanics describing $D0$ branes. The evidence for the conjecture consists of several correspondences between the two theories. As a consequence of supersymmetry the simple matrix model is rich enough to describe the properties of the entire Fock space of massless well separated particles of the supergravity theory. In one particular kinematic situation the leading large distance interaction of these particles is exactly described by supergravity. The model appears to be a nonperturbative realization of the holographic principle. The membrane states required by $M$ theory are contained as excitations of the matrix model. The membrane world volume is a noncommutative geometry embedded in a noncommutative spacetime.

/pdf/m-theory-as-a-matrix-model-a-conjecture-1zi5yivqwj.pdf

M theory as a matrix model: A conjecture

We explain how the string spectrum in flat space and pp-waves arises from the large-N limit, at fixed g2YM, of U(N) = 4 super Yang Mills. We reproduce the spectrum by summing a subset of the planar Feynman diagrams. We give a heuristic argument for why we can neglect other diagrams. We also discuss some other aspects of pp-waves and we present a matrix model associated to the DLCQ description of the maximally supersymmetric eleven dimensional pp-waves.

https://iopscience.iop.org/article/10.1088/1126-6708/2002/04/013/pdf

Strings in flat space and pp waves from Script N = 4 Super Yang Mills

Giant gravitons in AdS_5 x S^5, and its orbifolds, have a dual field theory representation as states created by chiral primary operators. We argue that these operators are not single-trace operators in the conformal field theory, but rather are determinants and subdeterminants of scalar fields; the stringy exclusion principle applies to these operators. Evidence for this identification comes from three sources: (a) topological considerations in orbifolds, (b) computation of protected correlators using free field theory and (c) a Matrix model argument. The last argument applies to AdS_7 x S^4 and the dual (2,0) theory, where we use algebraic aspects of the fuzzy 4-sphere to compute the expectation value of a giant graviton operator along the Coulomb branch of the theory.

Giant Gravitons in Conformal Field Theory

We identify a large family of 1/16 BPS operators in N=4 SYM that qualitatively reproduce the relations between charge, angular momentum and entropy in regular supersymmetric AdS_5 black holes when the main contribution to their masses is given by their angular momentum.

A Fermi Surface Model for Large Supersymmetric AdS_5 Black Holes

A supergravity dual of a (1,0) field theory in six dimensions

The Thirring model with random couplings is a translationally invariant generalisation of the SYK model to 1+1 dimensions, which is tractable in the large N limit. We compute its two point function, at large distances, for any strength of the random coupling. For a given realisation, the couplings contain both irrelevant and relevant marginal operators, but statistically, in the large N limit, the random couplings are overall always marginally irrelevant, in sharp distinction to the usual Thirring model. We show the leading term to the β function in conformal perturbation theory, which is quadratic in the couplings, vanishes, while its usually subleading cubic term matches our RG flow.

/pdf/comments-on-the-random-thirring-model-2xslyymdek.pdf

Comments on the random Thirring model

We examine the low-energy structure of N=1 supersymmetric SO(10) gauge theory with matter chiral superfields in N{sub Q} spinor and N{sub f} vector representations. We construct a dual to this model based upon an SU(N{sub f}+2N{sub Q}{minus}7){times}Sp(2N{sub Q}{minus}2) gauge group without utilizing deconfinement methods. This product theory generalizes all previously known Pouliot-type duals to SO(N{sub c}) models with spinor and vector matter. It also yields large numbers of new dual pairs along various flat directions. The dual description of the SO(10) theory satisfies multiple consistency checks including an intricate renormalization group flow analysis which links it with Seiberg{close_quote}s duality transformations. We discuss its implications for building grand-unified theories that contain all standard model fields as composite degrees of freedom. {copyright} {ital 1997} {ital The American Physical Society}

Micha Berkooz

Papers

Giant Gravitons in Conformal Field Theory

A Fermi Surface Model for Large Supersymmetric AdS_5 Black Holes

A supergravity dual of a (1,0) field theory in six dimensions

Comments on the random Thirring model

Dual descriptions of SO(10) supersymmetric gauge theories with arbitrary numbers of spinors and vectors