The Supermoduli Space of Matrix String Theory

TL;DR

This paper analyzes the moduli space of matrix string theory instantons and their fermionic supermoduli, revealing their structure and connection to the Weil-Petersson measure in the large N limit.

Contribution

It provides an explicit parameterization of the instanton moduli space and describes the fermionic supermoduli, linking matrix string theory to geometric structures on Riemann surfaces.

Findings

Explicit parameterization of instanton moduli space

Description of fermionic supermoduli set

Convergence of the measure to Weil-Petersson measure

Abstract

We study matrix string scattering amplitudes and matrix string instantons on a marked Riemann surface in the limit of a vanishing string coupling constant. We give an explicit parameterization of the moduli space of such instantons. We also give a description of the set of fermionic supermoduli. The integration over the supermoduli leads to the inclusion of picture changing operators at the interaction points. Finally we investigate the large N limit of the measure on the instanton moduli space and show its convergence to the Weil-Petersson measure on the moduli space of marked Riemann surfaces.