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

We study M-theory compactified on a specific class of seven-dimensional manifolds with SU(3) structure. The manifolds can be viewed as a fibration of an arbitrary Calabi-Yau threefold over a circle, with a U-duality twist around the circle. In some cases we find that in the four dimensional low energy effective theory a (broken) non-Abelian gauge group appears. Furthermore, such compactifications are shown to be dual to previously analyzed compactifications of the heterotic string on K3 × T 2 , with background gauge field fluxes on the T 2 .

Non-Abelian structures in compactifications of M-theory on seven-manifolds with SU(3) structure

The exact 2-point function of certain physically motivated operators in SYK-like spin glass models is computed, bypassing the Schwinger-Dyson equations. The models possess an IR low energy conformal window, but our results are exact at all time scales. The main tool developed is a new approach to the combinatorics of chord diagrams, allowing to rewrite the spin glass system using an auxiliary Hilbert space, and Hamiltonian, built on the space of open chord diagrams. We argue the latter can be interpreted as the bulk description and that it reduces to the Schwarzian action in the low energy limit.

/pdf/chord-diagrams-exact-correlators-in-spin-glasses-and-black-51y9pbj2hu.pdf

Chord diagrams, exact correlators in spin glasses and black hole bulk reconstruction

We suggest that the (2,0) six dimensional field theory compactified on $S^1\times K3$ is the Matrix model description of both M-theory on $K3$ and the Heterotic string on $T^3$. This proposal is different from existing proposals for the Heterotic theory. Different limits of the base space geometry give the different space-time interpretations, making M-theory/Heterotic duality manifest. We also present partial results on Heterotic/F-theory duality.

String Dualities from Matrix Theory

We show that configurations of multiple D-branes related by SU(N) rotations will preserve unbroken supersymmetry. This includes cases in which two D-branes are related by a rotation of arbitrarily small angle, and we discuss some of the physics of this. In particular, we discuss a way of obtaining 4D chiral fermions on the intersection of D-branes. 
We also rephrase the condition for unbroken supersymmety as the condition that a `generalized holonomy group' associated with the brane configuration and manifold is reduced, and relate this condition (in Type IIA string theory) to a condition in eleven dimensions.

Branes Intersecting at Angles

We present nontrivial examples of d = 3 gauge theories with sixteen and eight supercharges which are infrared dual at special points in the moduli space. This duality is distinct from mirror symmetry. To demonstrate duality we construct the gauge theories of interest using D2-branes and orientifolds and then consider their lift to M-theory. We also discuss the strong coupling limit of orientifold two-planes and orbifolds of orientifold six-planes.

/pdf/new-ir-dualities-in-supersymmetric-gauge-theory-in-three-3ejsgmon2z.pdf

Micha Berkooz

Papers

Non-Abelian structures in compactifications of M-theory on seven-manifolds with SU(3) structure

Chord diagrams, exact correlators in spin glasses and black hole bulk reconstruction

String Dualities from Matrix Theory

Branes Intersecting at Angles

New IR dualities in supersymmetric gauge theory in three dimensions