2D Yang-Mills Theory as a Matrix String Theory

TL;DR

This paper explores the quantization of 2D Yang-Mills theory on a torus, revealing twisted sectors analogous to string states in Matrix String Theory, and discusses a potential duality with the Gross-Taylor string.

Contribution

It introduces a new perspective on the partition function of 2D Yang-Mills, emphasizing twisted sectors and their relation to string theories, with improved interpretation and new results.

Findings

Twisted sectors correspond to torus coverings without branch points.

The partition function differs from the standard literature when these sectors are included.

A potential duality between the derived string theory and the Gross-Taylor string is proposed.

Abstract

Quantization of two-dimensional Yang-Mills theory on a torus in the gauge where the field strength is diagonal leads to twisted sectors that are completely analogous to the ones that originate long string states in Matrix String Theory. If these sectors are taken into account the partition function is different from the standard one found in the literature and the invariance of the theory under modular transformations of the torus appears to hold in a stronger sense. The twisted sectors are in one-to-one correspondence with the coverings of the torus without branch points, so they define by themselves a string theory. A possible duality between this string theory and the Gross-Taylor string is discussed, and the problems that one encounters in generalizing this approach to interacting strings are pointed out. This talk is based on a previous paper by the same authors, but it contains some new results and a better interpretation of the results already obtained.