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

We construct three dimensional Chern-Simons-matter theories with gauge groups U(N) × U(N) and SU(N) × SU(N) which have explicit = 6 superconformal symmetry. Using brane constructions we argue that the U(N) × U(N) theory at level k describes the low energy limit of N M2-branes probing a C4/Zk singularity. At large N the theory is then dual to M-theory on AdS4 × S7/Zk. The theory also has a 't Hooft limit (of large N with a fixed ratio N/k) which is dual to type IIA string theory on AdS4 × CP3. For k = 1 the theory is conjectured to describe N M2-branes in flat space, although our construction realizes explicitly only six of the eight supersymmetries. We give some evidence for this conjecture, which is similar to the evidence for mirror symmetry in d = 3 gauge theories. When the gauge group is SU(2) × SU(2) our theory has extra symmetries and becomes identical to the Bagger-Lambert theory.

N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals

This article reviews the generalization of field theory to space-time with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and string theory and to describe quantum Hall states. In the last few years they have been studied intensively, and many qualitatively new phenomena have been discovered, on both the classical and the quantum level.

Noncommutative field theory

Superstring theoryをめぐって(放談室)

Using the correspondence between gauge theories and string theory in curved backgrounds, we investigate aspects of the large-N limit of non-commutative gauge theories by considering gravity solutions with B fields. We argue that the total number of physical degrees of freedom at any given scale coincides with the commutative case. We then compute a two-point correlation function involving momentum components in the directions of the B-field. In the infrared regime it reproduces the usual behavior of the commutative gauge theory (i.e. of the form k4log k2). In the UV regime, we find that the two-point function decays exponentially with the momentum. A calculation of Wilson lines suggests that strings cannot be localized near the boundary. We also find string configurations that are localized in a finite region of the radial direction. These are worldsheet instantons.

https://iopscience.iop.org/article/10.1088/1126-6708/1999/09/025/pdf

Large N limit of non-commutative gauge theories

A general class of rotating closed string solutions in AdS5 × S 5 is shown to be described by a Neumann-Rosochatius one-dimensional integrable system. The latter represents an oscillator on a sphere or a hyperboloid with an additional “centrifugal” potential. We expect that the reduction of the AdS5 × S 5 sigma model to the Neumann-Rosochatius system should have further generalizations and should be useful for uncovering new relations between integrable structures on two sides of the AdS/CFT duality. We find, in particular, new circular rotating string solutions with two AdS5 and three S 5 spins. As in other recently discussed examples, the leading large-spin correction to the classical energy turns out to be proportional to the square of the string tension or the ’t Hooft coupling λ, suggesting that it can be matched onto the one-loop anomalous dimensions of the corresponding “long” operators on the SYM side of the AdS/CFT duality.

/pdf/spinning-strings-in-ads-5-s-5-new-integrable-system-40ylo68qyi.pdf

Spinning strings in AdS 5 × S 5 : New integrable system relations

We show that solitonic solutions of the classical string action on the AdS5 × S 5 background that carry charges (spins) of the Cartan subalgebra of the global symmetry group can be classified in terms of periodic solutions of the Neumann integrable system We derive equations which determine the energy of these solitons as a function of spins In the limit of large spins J, the first subleading 1/J coefficient in the expansion of the string energy is expected to be non-renormalised to all orders in the inverse string tension expansion and thus can be directly compared to the 1-loop anomalous dimensions of the corresponding composite operators in N = 4 super YM theory We obtain a closed system of equations that determines this subleading coefficient and, therefore, the 1-loop anomalous dimensions of the dual SYM operators We expect that an equivalent system of equations should follow from the thermodynamic limit of the algebraic Bethe ansatz for the SO(6) spin chain derived from SYM theory We also identify a particular string solution whose classical energy exactly reproduces the one-loop anomalous dimension of a certain set of SYM operators with two independent R charges J1, J2

Spinning strings in AdS5 × S5 and integrable systems

Spinning strings in AdS5 x S5 and integrable systems

The formation and semi-classical evaporation of two-dimensional black holes is studied in an exactly solvable model. Above a certain threshold energy flux, collapsing matter forms a singularity inside an apparent horizon. As the black hole evaporates the apparent horizon recedes and meets the singularity in a finite proper time. The singularity emerges naked and future evolution of the geometry requires boundary conditions to be imposed there. There is a natural choice of boundary conditions which match the evaporated black hole solution onto the linear dilaton vacuum. Below the threshold energy flux no horizon forms and boundary conditions can be imposed where infalling matter is reflected from a time-like naked singularity. All information is recovered at spatial infinity in this case.

/pdf/end-point-of-hawking-radiation-5fq15f332l.pdf

Jorge G. Russo

Papers

Large N limit of non-commutative gauge theories

Spinning strings in AdS 5 × S 5 : New integrable system relations

Spinning strings in AdS5 × S5 and integrable systems

Spinning strings in AdS5 x S5 and integrable systems

End point of Hawking radiation