Perturbative Vacua from IIB Matrix Model

TL;DR

This paper demonstrates that the IIB matrix model can describe various vacua of string theory, including type IIA, by using a quenching procedure that relates it to matrix string theory in the large N limit.

Contribution

It shows how to realize type IIA string theory vacua within the IIB matrix model through quenching and large N limits, connecting matrix models to string theory.

Findings

The moduli space of diagonal matrices corresponds to perturbatively stable string vacua.

Quenching diagonal elements relates the IIB matrix model to matrix string theory.

The large N limit of the quenched IIB matrix model reproduces type IIA string theory.

Abstract

It has not been clarified whether a matrix model can describe various vacua of string theory. In this paper, we show that the IIB matrix model includes type IIA string theory. In the naive large N limit of the IIB matrix model, configurations consisting of simultaneously diagonalizable matrices form a moduli space, although the unique vacuum would be determined by complicated dynamics. This moduli space should correspond to a part of perturbatively stable vacua of string theory. Actually, one point on the moduli space represents type IIA string theory. Instead of integrating over the moduli space in the path-integral, we can consider each of the simultaneously diagonalizable configurations as a background and set the fluctuations of the diagonal elements to zero. Such procedure is known as quenching in the context of the large N reduced models. By quenching the diagonal elements of the matrices to an appropriate configuration, we show that the quenched IIB matrix model is equivalent to the two-dimensional large N N=8 super Yang-Mills theory on a cylinder. This theory is nothing but matrix string theory and is known to be equivalent to type IIA string theory. As a result, we find the manner to take the large N limit in the IIB matrix model.