Matrix string states in pure 2d Yang Mills theories

TL;DR

This paper quantizes pure 2d Yang-Mills theory on a torus, revealing string-like states that relate to Matrix string theory and discussing their role in modular invariance.

Contribution

It introduces string-like states in 2d Yang-Mills theory spectrum and generalizes the partition function, connecting to Matrix string theory.

Findings

Identification of string-like states due to topological obstructions

Explicit form of the generalized partition function

Discussion on the role of states in modular invariance

Abstract

We quantize pure 2d Yang-Mills theory on a torus in the gauge where the field strength is diagonal. Because of the topological obstructions to a global smooth diagonalization, we find string-like states in the spectrum similar to the ones introduced by various authors in Matrix string theory. We write explicitly the partition function, which generalizes the one already known in the literature, and we discuss the role of these states in preserving modular invariance. Some speculations are presented about the interpretation of 2d Yang-Mills theory as a Matrix string theory.