Generalized two-dimensional Yang-Mills theory is a matrix string theory

TL;DR

This paper introduces a generalized two-dimensional Yang-Mills theory that incorporates coupling to two-dimensional gravity, leading to a natural interpretation as a Matrix String Theory involving covering maps from world-sheets to Riemann surfaces.

Contribution

It extends 2D Yang-Mills theory by coupling it to gravity and demonstrates its interpretation as a Matrix String Theory with topological sectors.

Findings

The generalized theory matches ordinary Yang-Mills on flat surfaces.

Quantization in the unitary gauge accounts for all topological sectors.

The resulting framework interprets the theory as a covering map from world-sheet to target surface.

Abstract

We consider two-dimensional Yang-Mills theories on arbitrary Riemann surfaces. We introduce a generalized Yang-Mills action, which coincides with the ordinary one on flat surfaces but differs from it in its coupling to two-dimensional gravity. The quantization of this theory in the unitary gauge can be consistently performed taking into account all the topological sectors arising from the gauge-fixing procedure. The resulting theory is naturally interpreted as a Matrix String Theory, that is as a theory of covering maps from a two-dimensional world-sheet to the target Riemann surface.