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

Large N Field Theories, String Theory and Gravity

QUANTUM gravitational effects are usually ignored in calculations of the formation and evolution of black holes. The justification for this is that the radius of curvature of space-time outside the event horizon is very large compared to the Planck length (Għ/c3)1/2 ≈ 10−33 cm, the length scale on which quantum fluctuations of the metric are expected to be of order unity. This means that the energy density of particles created by the gravitational field is small compared to the space-time curvature. Even though quantum effects may be small locally, they may still, however, add up to produce a significant effect over the lifetime of the Universe ≈ 1017 s which is very long compared to the Planck time ≈ 10−43 s. The purpose of this letter is to show that this indeed may be the case: it seems that any black hole will create and emit particles such as neutrinos or photons at just the rate that one would expect if the black hole was a body with a temperature of (κ/2π) (ħ/2k) ≈ 10−6 (M/M)K where κ is the surface gravity of the black hole1. As a black hole emits this thermal radiation one would expect it to lose mass. This in turn would increase the surface gravity and so increase the rate of emission. The black hole would therefore have a finite life of the order of 1071 (M/M)−3 s. For a black hole of solar mass this is much longer than the age of the Universe. There might, however, be much smaller black holes which were formed by fluctuations in the early Universe2. Any such black hole of mass less than 1015 g would have evaporated by now. Near the end of its life the rate of emission would be very high and about 1030 erg would be released in the last 0.1 s. This is a fairly small explosion by astronomical standards but it is equivalent to about 1 million 1 Mton hydrogen bombs. It is often said that nothing can escape from a black hole. But in 1974, Stephen Hawking realized that, owing to quantum effects, black holes should emit particles with a thermal distribution of energies — as if the black hole had a temperature inversely proportional to its mass. In addition to putting black-hole thermodynamics on a firmer footing, this discovery led Hawking to postulate 'black hole explosions', as primordial black holes end their lives in an accelerating release of energy.

Black Hole Explosions

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

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

These notes are loosely based on lectures given at the CERN Winter School on Supergravity, Strings and Gauge theories, February 2009, and at the IPM String School in Tehran, April 2009. I have focused on a few concrete topics and also on addressing questions that have arisen repeatedly. Background condensed matter physics material is included as motivation and easy reference for the high energy physics community. The discussion of holographic techniques progresses from equilibrium, to transport and to superconductivity.

https://iopscience.iop.org/article/10.1088/0264-9381/26/22/224002/pdf

Lectures on holographic methods for condensed matter physics

It is natural to believe that the free symmetric product orbifold CFT is dual to the tensionless limit of string theory on AdS3 × S3 × $$ {\mathbb{T}}^4 $$
 . At this point in moduli space, string theory is expected to contain a Vasiliev higher spin theory as a subsector. We confirm this picture explicitly by showing that the large level limit of the $$ \mathcal{N} $$
 =4 cosets of arXiv:1305.4181, that are dual to a higher spin theory on AdS3, indeed describe a closed subsector of the symmetric product orbifold. Furthermore, we reorganise the full partition function of the symmetric product orbifold in terms of representations of the higher spin algebra (or rather its $$ {\mathcal{W}}_{\infty } $$
 extension). In particular, the unbroken stringy symmetries of the tensionless limit are captured by a large chiral algebra which we can describe explicitly in terms of an infinite sum of $$ {\mathcal{W}}_{\infty } $$
 representations, thereby exhibiting a vast extension of the conventional higher spin symmetry.

Higher spins & strings

The partition function of the $ {\mathcal{W}_N} $
 minimal model CFT is computed in the large N ’t Hooft limit and compared to the spectrum of the proposed holographic dual, a 3d higher spin gravity theory coupled to massive scalar fields. At finite N, the CFT contains additional light states that are not visible in the perturbative gravity theory. We carefully define the large N limit, and give evidence that, at N = ∞, the additional states become null and decouple from all correlation functions. The surviving states are shown to match precisely (for all values of the ’t Hooft coupling) with the spectrum of the higher spin gravity theory. The agreement between bulk and boundary is partially explained by symmetry considerations involving the conjectured equivalence between the $ {\mathcal{W}_N} $
 algebra in the large N limit and the higher spin algebra of the Vasiliev theory.

/pdf/partition-functions-of-holographic-minimal-models-4qd0q7v75k.pdf

Partition functions of holographic minimal models

It is conjectured that strongly coupled, spatially noncommutative $\mathcal{N}=4$ Yang-Mills theory has a dual description as a weakly coupled open string theory in a near critical electric field, and that this dual theory is fully decoupled from closed strings. Evidence for this conjecture is given by the absence of physical closed string poles in the non-planar one-loop open string diagram. The open string theory can be viewed as living in a geometry in which space and time coordinates do not commute.

S-Duality and Noncommutative Gauge Theory

Superstring theory on $$ {\mathrm{AdS}}_3 \times {S}^3\times {\mathbb{T}}^4 $$
 with the smallest amount of NS-NS flux (“k = 1”) is shown to be dual to the spacetime CFT given by the large N limit of the free symmetric product orbifold SymN
 $$ \left({\mathbb{T}}^4\right) $$
 . To define the worldsheet theory at k = 1, we employ the hybrid formalism in which the AdS3 × S3 part is described by the $$ \mathfrak{p}\mathfrak{s}\mathfrak{u}{\left(1,1\Big|2\right)}_1 $$
 WZW model (which is well defined). Unlike the case for k ≥ 2, it turns out that the string spectrum at k = 1 does not exhibit the long string continuum, and perfectly matches with the large N limit of the symmetric product. We also demonstrate that the fusion rules of the symmetric orbifold are reproduced from the worldsheet perspective. Our proposal therefore affords a tractable worldsheet description of a tensionless limit in string theory, for which the dual CFT is also explicitly known.

/pdf/the-worldsheet-dual-of-the-symmetric-product-cft-43l9fnt38c.pdf

The worldsheet dual of the symmetric product CFT

Open string theories can be decoupled from closed strings and gravity by scaling to the critical electric field. We propose dual descriptions for the strong coupling limit of these NCOS (Non-Commutative Open String) theories in six or fewer spacetime dimensions. In particular, we conjecture that the 5-dimensional NCOS theory at strong coupling, is a theory of light Open Membranes (OM), decoupled from gravity, on an M5-brane with a near-critical three-form field strength. The relation of OM theory to NCOS theories resembles that of M-theory to type-II closed string theories. In two dimensions we conjecture that supersymmetric U(n) gauge theory with a unit of electric flux is dual to the NCOS theory with string coupling 1/n. A construction based on NS5-branes leads to new theories in six dimensions generalising the little string theory. A web of dualities relates all the above theories when they are compactified on tori.

Rajesh Gopakumar

Papers

Higher spins & strings

Partition functions of holographic minimal models

S-Duality and Noncommutative Gauge Theory

The worldsheet dual of the symmetric product CFT

OM theory in diverse dimensions