Collective field theory of a singular supersymmetric matrix model

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.

Physics Letters B, 1991

We generalize the collective field theory to include supersymmetry. This provides a field theory of supersymmetric non-critical strings. We demonstrate supersymmetry at the operator level. In studying small fluctuations a massless Majorana fermion is found as a partner to the tachyon.

Physics Letters B, 1992

We generalize the Marinari-Parisi definition for pure two dimensional quantum gravity (k = 2) to all non unitary minimal multicritical points (k ≥ 3). The resulting interacting Fermi gas theory is treated in the collective field framework. Making use of the fact that the matrices evolve in Langevin time, the Jacobian from matrix coordinates to collective modes is similar to the corresponding Jacobian in d = 1 matrix models. The collective field theory is analyzed in the planar limit. The saddle point eigenvalue distribution is the one that defines the original multicritical point and therefore exhibits the appropriate scaling behaviour. Some comments on the nonperturbative properties of the collective field theory as well as comments on the Virasoro constraints associated with the loop equations are made at the end of this letter. There we also make some remarks on the fermionic formulation of the model and its integrability, as a nonlocal version of the non linear Schrödinger model.

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

Journal of High Energy Physics, 2006

We present a method for solving BPS equations obtained in the collective-field approach to matrix models. The method enables us to find BPS solutions and quantum excitations around these solutions in the one-matrix model, and in general for the Calogero model. These semiclassical solutions correspond to giant gravitons described by matrix models obtained in the framework of AdS/CFT correspondence. The two-field model, associated with two types of giant gravitons, is investigated. In this duality-based matrix model we find the finite form of the n-soliton solution. The singular limit of this solution is examined and a realization of open-closed string duality is proposed.

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.

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.

International Journal of Modern Physics A, 2004

We develop a systematic procedure for deriving canonical string field theory from large N matrix models in the Berenstein-Maldacena-Nastase limit. The approach, based on collective field theory, provides a generalization of standard string field theory.