2D string theory as normal matrix model

Journal of High Energy Physics, 2005

We give an explicit demonstration of the equivalence between the Normal Matrix Model (NMM) of c = 1 string theory at selfdual radius and the Kontsevich-Penner (KP) model for the same string theory. We relate macroscopic loop expectation values in the NMM to condensates of the closed string tachyon, and discuss the implications for open-closed duality. As in c < 1, the Kontsevich-Miwa transform between the parameters of the two theories appears to encode open-closed string duality, though our results also exhibit some interesting differences with the c < 1 case. We also briefly comment on two different ways in which the Kontsevich model originates.

Physics Letters B, 1995

We show that the most general two-matrix model with bilinear coupling underlies c = 1 string theory. More precisely we prove that W 1+∞ constraints, a subset of the correlation functions and the integrable hierarchy characterizing such twomatrix model, correspond exactly to the W 1+∞ constraints, to the discrete tachyon correlation functions and to the integrable hierarchy of the c = 1 string theory.

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.

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, 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

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.

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

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.

1995

We show how the two-matrix model and Toda lattice hierarchy presented in a previous paper can be solved exactly: we obtain compact formulas for correlators of pure tachyonic states at every genus. We then extend the model to incorporate a set of discrete states organized in finite dimensional sl 2 representations. We solve also this extended model and find the correlators of the discrete states by means of the W constraints and the flow equations. Our results coincide with the ones existing in the literature in those cases in which particular correlators have been explicitly calculated. We conclude that the extented two-matrix model is a realization of the discrete states of c = 1 string theory. *

Nuclear Physics B, 1995

The user has requested enhancement of the downloaded file. arXiv:hep-th/9505127v2 28 Jun 1995 hep-th/9505127 ABSTRACT We derive a Kontsevich-type matrix model for the c = 1 string directly from the W ∞ solution of the theory. The model that we obtain is different from previous proposals, which are proven to be incorrect. Our matrix model contains the Penner and Kontsevich cases, and we study its quantum effective action. The simplicity of our model leads to an encouraging interpretation in the context of background-independent non-critical string field theory.