Spenta R. Wadia

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 ).

Forced fluid dynamics from gravity

We generalize the computations of [1] to generate long wavelength, asymptotically locally AdS5 solutions to the Einstein-dilaton system with a slowly varying boundary dilaton field and a weakly curved boundary metric. Upon demanding regularity , our solutions are dual, under the AdS/CFT correspondence, to arbitrary fluid flows in the boundary theory formulated on a weakly curved manifold with a prescribed slowly varying coupling constant. These solutions turn out to be parameterized by four-velocity and temperature fields that are constrained to obey the boundary covariant Navier Stokes equations with a dilaton dependent forcing term. We explicitly evaluate the stress tensor and Lagrangian as a function of the velocity, temperature, coupling constant and curvature fields, to second order in the derivative expansion and demonstrate the Weyl covariance of these expressions. We also construct the event horizon of the dual solutions to second order in the derivative expansion, and use the area form on this event horizon to construct an entropy current for the dual fluid. As a check of our constructions we expand the exactly known solutions for rotating black holes in global AdS5 in a boundary derivative expansion and find perfect agreement with all our results upto second order. We also find other simple solutions of the forced fluid mechanics equations and discuss their bulk interpretation. Our results may aid in determining a bulk dual to forced flows exhibiting steady state turbulence.

N = ∞ phase transition in a class of exactly soluble model lattice gauge theories

Abstract An exactly soluble class of model U ( N ) lattice gauge theories is considered. The ground state is discussed as a separable N -fermion problem solved by mathieu functions. Some exact correlation functions are presented. The N = ∞ limit exhibits a third order phase transition demarcating the strong and weak phases at ( g 2 N ) −1 ≈ 0.55.

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).

Gauge theory on a quantum phase space

In this Letter we present a operator formulation of gauge theories in a quantum phase space which is specified by a operator algebra. For simplicity we work with the Heisenberg algebra. We introduce the notion of the derivative (transport) and Wilson line (parallel transport) which enables us to construct a gauge theory in a simple way. We illustrate the formulation by a discussion of the Higgs mechanism and comment on the large N masterfield.

Finite temperature effective action, AdS 5 black holes, and 1/N expansion

We propose a phenomenological matrix model to study string theory in AdS5 × S5 in the canonical ensemble. The model reproduces all the known qualitative features of the theory. In particular, it gives a simple effective potential description of Euclidean black hole nucleation and the tunnelling between thermal AdS and the big black hole. It also has some interesting predictions. We find that there exists a critical temperature at which the Euclidean small black hole undergoes a Gross-Witten phase transition. We identify the phase transition with the Horowitz-Polchinski point where the black hole horizon size becomes comparable to the string scale. The appearance of the Hagedorn divergence of thermal AdS is due to the merger of saddle points corresponding to the Euclidean small black hole and thermal AdS. The merger can be described in terms of a cusp (A3) catastrophe and divergences at the perturbative string level are smoothed out at finite string coupling using standard techniques of catastrophe theory.

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.

Quantization of the Liouville Mode and String Theory

We discuss the space-time interpretation of bosonic string theories, which involve d scalar fields coupled to gravity in two dimensions, with a proper quantization of the world-sheet metric. We show that for d>25, the theory cannot describe string modes consistently coupled to each other. For d=25 this is possible; however, in this case the Liouville mode acts as an extra timelike variable and one really has a string moving in 26-dimensional space-time with a Lorentzian signature. By analyzing such a string theory in background fields, we show that the d=25 theory possesses the full 26-dimensional general covariance.

EXCITATIONS AND INTERACTIONS IN d=1 STRING THEORY

We discuss the singlet sector of the d=1 matrix model in terms of a Dirac fermion formalism. The leading order two- and three-point functions of the density fluctuations are obtained by this method. This allows us to construct the effective action to that order and hence provide the equation of motion. This equation is compared with the one obtained from the continuum approach. We also compare continuum results for correlation functions with the matrix model ones and discuss the nature of gravitational dressing for this regularization. Finally, we address the question of boundary conditions within the framework of the d=1 unitary matrix model, considered as a regularized version of the Hermitian model, and study the implications of a generalized action with an additional parameter (analogous to the θ parameter) which give rise to quasi-periodic wave functions.