Matrix String Theory and its Moduli Space

TL;DR

This paper constructs instanton solutions in Matrix String Theory, revealing how its moduli space approximates the string interaction moduli space at large N, thus connecting nonperturbative gauge theory solutions with string theory geometry.

Contribution

It provides a detailed construction of instanton solutions in Matrix String Theory and analyzes the finite N moduli space, showing its discretization and convergence to the string moduli space as N approaches infinity.

Findings

Finite N moduli space is a discretized version of the string moduli space.

As N increases, the discrete dimensions become continuous.

The instanton solutions interpolate between initial and final string configurations.

Abstract

The correspondence between Matrix String Theory in the strong coupling limit and IIA superstring theory can be shown by means of the instanton solutions of the former. We construct the general instanton solutions of Matrix String Theory which interpolate between given initial and final string configurations. Each instanton is characterized by a Riemann surface of genus h with n punctures, which is realized as a plane curve. We study the moduli space of such plane curves and find out that, at finite N, it is a discretized version of the moduli space of Riemann surfaces: instead of 3h-3+n its complex dimensions are 2h-3+n, the remaining h dimensions being discrete. It turns out that as $N$ tends to infinity, these discrete dimensions become continuous, and one recovers the full moduli space of string interaction theory.