Large $N$ Phases of Chiral QCD_2

TL;DR

This paper constructs a matrix model for a chiral large N gauge theory on a 2D sphere, revealing three phases, and derives a simple formula for counting certain covering maps in the large area phase.

Contribution

It introduces a matrix model for chiral large N QCD in two dimensions and provides an exact free energy expression to count sphere coverings with fixed branch points.

Findings

Identification of three distinct phases in the model.

Exact free energy expression in the large area phase.

Simple formula for counting topologically inequivalent sphere coverings.

Abstract

A matrix model is constructed which describes a chiral version of the large $N$ $U(N)$ gauge theory on a two-dimensional sphere of area $A$. This theory has three separate phases. The large area phase describes the associated chiral string theory. An exact expression for the free energy in the large area phase is used to derive a remarkably simple formula for the number of topologically inequivalent covering maps of a sphere with fixed branch points and degree $n$.