A Matrix Model for the 2d Black Hole

2000

We construct a large N matrix matrix model describing two-dimensional Euclidean string theory compactified on a circle of radius R and perturbed by an operator creating winding modes (vortices) on the worldsheet. The matrix model is exactly solvable and posesses an integrable structure of the infinite Toda chain hierarchy. We give explicit expressions for its free energy in the sphere-and torus approximation. A conjecture by V. Fateev, A. and Al. Zamolodchikov about the equivalence of the sine-Liouville and SL(2, R)/U(1) conformal field theories implies that for particular values of the parameters (vanishing cosmological constant µ and compactification radius R = 3 4 R KT ) the matrix model can be used to study two-dimensional string theory in the Euclidean black hole background to all orders in string perturbation theory.

Nuclear Physics B, 2002

We construct and study a matrix model that describes two dimensional string theory in the Euclidean black hole background. A conjecture of V. Fateev, A. and Al. Zamolodchikov, relating the black hole background to condensation of vortices (winding modes around Euclidean time) plays an important role in the construction. We use the matrix model to study quantum corrections to the thermodynamics of two dimensional black holes.

2013

In this talk, we first review the possibility of matrix models toward a nonperturbative (critical) string theory. We then discuss whether the c = 1 matrix model can describe the black hole solution of 2D critical string theory. We show that there exists a class of integral transformations which send the Virasoro condition for the tachyon field around the 2D black hole to that around the linear dilaton vacuum. In particular, we construct an explicit integral formula wihich describes a continuous deformation of the linear dilaton vacuum to the black hole background. Contents 1. Introduction: Basic

Nuclear Physics B, 1994

We invesigate how the exact 2D black-hole solution for the critical string theory should be described, at least perturbatively with respect to the inverse mass of the black hole, within the framework of matrix model. In particular, we propose a working hypothesis on the basis of which we can present plausible candidates for the necessary non-local field redefinition of the tachyon field and the deformation of the usual c = 1 matrix model with µ = 0. We exhibit some marked difference in the properties of tachyon scattering of the deformed model from those of the usual c = 1 model corresponding to tachyon condensation. These results lead to a concrete proposal for the S-matrix for the tachyon

Nuclear Physics B, 2003

We show that the c = 1 bosonic string theory at finite temperature has two matrixmodel realizations related by a kind of duality transformation. The first realization is the standard one given by the compactified matrix quantum mechanics in the inverted oscillator potential. The second realization, which we derive here, is given by the normal matrix model. Both matrix models exhibit the Toda integrable structure and are associated with two dual cycles (a compact and a non-compact one) of a complex curve with the topology of a sphere with two punctures. The equivalence of the two matrix models holds for an arbitrary tachyon perturbation and in all orders in the string coupling constant.

Arxiv preprint hep-th/9211085, 1992

We discuss the basic features of the double scaling limit of the one dimensional matrix model and its interpretation as a two dimensional string theory. Using the collective field theory formulation of the model we show how the fluctuations of the collective field can be interpreted as the massless "tachyon" of the two dimensional string in a linear dilaton background. We outline the basic physical properties of the theory and discuss the nature of the Smatrix. Finally we show that the theory admits of another interpretation in which a certain integral transform of the collective field behaves as the massless "tachyon" in the two dimensional string with a blackhole background. We show that both the classical background and the fluctuations are non-singular at the black hole singularity.

String Theory in a Nutshell, 2011

It is generally accepted that the double-scaled 1D matrix model is equivalent to the c = 1 string theory with tachyon condensation. There remain however puzzles that are to be claried in order to utilize this connection for our quest towards possible non-perturbative formulation of string theory. W e discuss some of the issues that are related to the space-time interpretation of matrix models, in particular, the questions of leg poles, causality, and black hole background. Finally, a speculation about a possible connection of a deformed matrix model with the idea of Dirichret brane is presented.

Nuclear Physics B, 1997

Via compactification on a circle, the matrix model of M-theory proposed by Banks et al suggests a concrete identification between the large N limit of two-dimensional N = 8 supersymmetric Yang-Mills theory and type IIA string theory. In this paper we collect evidence that supports this identification. We explicitly identify the perturbative string states and their interactions, and describe the appearance of D-particle and D-membrane states. * Here we work in string units α = 1. A derivation of (1) from matrix theory and a discussion of our normalizations is given in the appendix.

Nuclear Physics B, 1993

We show that a special superconformal coset (withĉ = 3) is equivalent to c = 1 matter coupled to two dimensional gravity. This identification allows a direct computation of the correlation functions of the c = 1 non-critical string to all genus, and at nonzero cosmological constant, directly from the continuum approach. The results agree with those of the matrix model. Moreover we connect our coset with a twisted version of a Euclidean two dimensional black hole, in which the ghost and matter systems are mixed.

Physical Review D, 1993

In this paper we investigate in more detail our previous formulation of the dilaton-gravity theory by Bilal-Callan-de Alwis as a SL 2 -conformal affine Toda (CAT) theory. Our main results are: