Matrix string theory

Abstract

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.

Comments on Supersymmetry Algebra and Contact Term in Matrix String Theory

“…Let us turn to the matrix string theory [8]. The matrix string theory proposal was motivated by compactifying [16][7] M(atrix) theory [17] on one dimension.…”

“…Note that, conceptually we have already known the result, because at this order the supersymmetry algebra was worked out in the light-cone superstring field theory by [9], and its relation to the matrix string theory was explored by [6]. Technically, the supersymmetry algebra was mostly worked out in the original paper [8], except a few details about including both the holomorphic and anti-holomorphic parts and about confirming the independence between two supercharges (2.6). However, we believe that it is important to make the leading order supersymmetry algebra clear at this point.…”

Supergravity Duals of Matrix String Theory

“…The natural candidates for such dual theories in the case of D-strings are the orbifold SCFT's [6,9] to which the two-dimensional gauge theories governing the dynamics of D-strings in type IIB and type I theory flow in the infrared. They can be thought as second quantized type II or heterotic strings moving on (R 8 ) N /S N .…”

“…The case of D-strings is particular to type IIB and type I theory and will be the main subject of our investigation. The dual gauge theories in these cases correspond to the matrix string models [6,7] proposed as non-perturbative definitions of type IIA and heterotic string theories. The correspondences under study here in principle provide a supergravity description of this physics (see [8] for early discussions on these ideas).…”

A matrix model for the null-brane

“…This Lagrangian (65) describes M-theory on the null-brane. However, in agreement with the supergravity solution (15), the model is described by a kind of Matrix string theory [32][33][34] near τ = 0. On the other hand, as |τ | → ∞, fluctuations in θ are suppressed and the model reduces to quantum mechanics.…”