Gautam Mandal

CLASSICAL SOLUTIONS OF 2-DIMENSIONAL STRING THEORY

We present an exact one-parameter family of solutions to the classical graviton-dilaton system in two dimensions. The solution can be identified as a black hole. We present the solution both in a Schwarzschild-like gauge and in the target space conformal gauge. We discuss possible relations with matrix models.

Microscopic formulation of black holes in string theory

Abstract In this report we review the microscopic formulation of the five-dimensional black hole of type IIB string theory in terms of the D1–D5 brane system. The emphasis here is more on the brane dynamics than on supergravity solutions. We show how the low energy brane dynamics, combined with crucial inputs from AdS/CFT correspondence, leads to a derivation of black hole thermodynamics and the rate of Hawking radiation. Our approach requires a detailed exposition of the gauge theory and conformal field theory of the D1–D5 system. We also discuss some applications of the AdS/CFT correspondence in the context of black hole formation in three dimensions by thermal transition and by collision of point particles.

Aspects of semiclassical strings in AdS5

Abstract We find an infinite number of conserved currents and charges in the semiclassical limit λ →∞ of string theory in AdS 5 × S 5 and remark on their relevance to conserved charges in the dual gauge theory. We establish a general procedure of exploring the semiclassical limit by viewing the classical motion as collective motion in the relevant part of the configuration space. We illustrate the procedure for semiclassical expansion around solutions of string theory on AdS 5 ×( S 5 / Z M ).

Local fluid dynamical entropy from gravity

Spacetime geometries dual to arbitrary fluid flows in strongly coupled N=4 super Yang Mills theory have recently been constructed perturbatively in the long wavelength limit. We demonstrate that these geometries all have regular event horizons, and determine the location of the horizon order by order in a boundary derivative expansion. Intriguingly, the derivative expansion allows us to determine the location of the event horizon in the bulk as a local function of the fluid dynamical variables. We define a natural map from the boundary to the horizon using ingoing null geodesics. The area-form on spatial sections of the horizon can then be pulled back to the boundary to define a local entropy current for the dual field theory in the hydrodynamic limit. The area theorem of general relativity guarantees the positivity of the divergence of the entropy current thus constructed.

Absorption versus decay of black holes in string theory and T-symmetry

Abstract Classically a black hole can absorb but not emit energy. We discuss how this T-asymmetric property of black holes arises in the recently proposed (T-symmetric) microscopic models of black holes based on bound states of D-branes. In these string theory based models, the nonvanishing classical absorption is made possible essentially by the exponentially increasing degeneracy of quantum states with mass of the black hole. The classical limit of the absorption cross section computed in the microscopic model agrees with the result obtained from a classical analysis of a wave propagating in the background metric of the corresponding black hole (upto a numerical factor).

A c-function for non-supersymmetric attractors

We present a c-function for spherically symmetric, static and asymptotically flat solutions in theories of four-dimensional gravity coupled to gauge fields and moduli. The c-function is valid for both extremal and non-extremal black holes. It monotonically decreases from infinity and in the static region acquires its minimum value at the horizon, where it equals the entropy of the black hole. Higher dimensional cases, involving p-form gauge fields, and other generalisations are also discussed.

Counting 1/8-BPS dual-giants

We count 1/8-BPS states in type IIB string theory on AdS5 × S 5 background which carry three independent angular momenta on S 5 . These states can be counted by considering configurations of multiple dual-giant gravitons up to N in number which share at least four supersymmetries. We map this counting problem to that of counting the energy eigenstates of a system of N bosons in a 3-dimensional harmonic oscillator. We also count 1/8-BPS states with two independent non-zero spins in AdS5 and one non-zero angular momentum on S 5 by considering configurations of arbitrary number of giant gravitons that share at least four supersymmetries.

Nielsen-Olesen vortices in noncommutative abelian Higgs model

We construct Nielsen-Olesen vortex solution in the noncommutative abelian Higgs model. We derive the quantized topological flux of the vortex solution. We find that the flux is integral by explicit computation in the large-θ limit as well as in the small-θ limit. In the context of a tachyon vortex on the brane-antibrane system we demonstrate that it is this topological charge that gives rise to the RR charge of the resulting BPS D-brane. We also consider the left-right-symmetric gauge theory which does not have a commutative limit and construct an exact vortex solution in it.

Supergravity description of non-Bogomol’nyi-Prasad-Sommerfield branes

We construct supergravity solutions that correspond to N Dp-branes coinciding with N Dp-branes. We study the physical properties of the solutions and analyse the supergravity description of tachyon condensation. We construct an interpolation between the brane-antibrane solution and the Schwarzschild solution and discuss its possible application to the study of non-supersymmetric black holes. May 2000 e-mail: Philippe.Brax@cern.ch, Gautam.Mandal@cern.ch, Yaron.Oz@cern.ch

Gregory-Laflamme as the confinement/deconfinement transition in holographic QCD

We discuss the phase structure of N D4 branes wrapped on a temporal (Euclidean) and a spatial circle, in terms of the near-horizon AdS geometries. This system has been studied previously to understand four dimensional pure SU(N) Yang-Mills theory (YM4) through holography. In the usual treatment of the subject, the phase transition between the AdS soliton and the black D4 brane is interpreted as the strong coupling continuation of the confinement/deconfinement transition in YM4. We show that this interpretation is not valid, since the black D4 brane and the deconfinement phase of YM4 have different realizations of the ZN centre symmetry and cannot be identified. We propose an alternative gravity dual of the confinement/deconfinement transition in terms of a Gregory-Laflamme transition of the AdS soliton in the IIB frame, where the strong coupling continuation of the deconfinement phase of YM4 is a localized D3 soliton. Our proposal offers a new explanation of several aspects of the thermodynamics of holographic QCD. As an example, we show a new mechanism of chiral symmetry restoration in the Sakai-Sugimoto model. The issues discussed in this paper pertain to gravity duals of non-supersymmetric gauge theories in general.