The C = 1 Matrix Model Formulation of Two Dimensional Yang-Mills Theories

TL;DR

This paper derives an exact matrix model description for two-dimensional Yang-Mills theories with arbitrary gauge groups, revealing connections to integrable systems and fermionic models, and providing explicit partition functions.

Contribution

It introduces a novel matrix model formulation for 2D Yang-Mills theories on various surfaces, linking gauge theories to integrable fermionic systems and deriving exact partition functions.

Findings

Exact matrix model for 2D Yang-Mills on cylinder and torus

Connection between gauge theories and Sutherland fermions

Explicit grand canonical partition functions for classical groups

Abstract

We find the exact matrix model description of two dimensional Yang-Mills theories on a cylinder or on a torus and with an arbitrary compact gauge group. This matrix model is the singlet sector of a $c =1$ matrix model where the matrix field is in the fundamental representation of the gauge group. We also prove that the basic constituents of the theory are Sutherland fermions in the zero coupling limit, and this leads to an interesting connection between two dimensional gauge theories and one dimensional integrable systems. In particular we derive for all the classical groups the exact grand canonical partition function of the free fermion system corresponding to a two dimensional gauge theory on a torus.