A matrix model for the two-dimensional black hole

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

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.

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

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.

Journal of High Energy Physics, 2003

Modern Physics Letters A, 1992

We discuss the classical two-dimensional black hole in the framework of the non-perturbative formulation (in terms of non-relativistic fermions) of c=1 string field theory. We identify an off-shell operator whose classical equation of motion is that of tachyon in the classical graviton-dilaton black hole background. The black hole ‘singularity’ is identified with the Fermi surface in the phase space of a single fermion, and as such is a consequence of the semiclassical approximation. An exact treatment reveals that stringy quantum effects wash away the classical singularity.

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.

2016

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 clarified in order to utilize this connection for our quest towards possible non-perturbative formulation of string theory. We 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.

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.

Eprint Arxiv Hep Th 9503125, 1995

We present a brief overview of 2-dim. string theory and its connection to the theory of non-relativistic fermions in one dimension. We emphasize (i) the role of W ∞ algebra and (ii) the modelling of some aspects of 2-dim. black hole physics using the phase space representation of the fermi fluid.