Evaluation of the Free Energy of Two-Dimensional Yang-Mills Theory

TL;DR

This paper evaluates the free energy of 2D Yang-Mills theory on a sphere for SO(N) and Sp(N) groups in the weak-coupling phase using 1/N expansion, highlighting universal and group-specific features.

Contribution

It applies the 1/N expansion technique to compute free energy for different gauge groups, revealing both universal and distinct subleading behaviors.

Findings

Universal features in large N limit across gauge groups

Differences in subleading 1/N corrections between SO(N) and Sp(N)

Evaluation of free energy in weak-coupling phase

Abstract

The free energy in the weak-coupling phase of two-dimensional Yang-Mills theory on a sphere for SO(N) and Sp(N) is evaluated in the 1/N expansion using the techniques of Gross and Matytsin. Many features of Yang-Mills theory are universal among different gauge groups in the large N limit, but significant differences arise in subleading order in 1/N.