Wilson loop for large N Yang-Mills theory on a two-dimensional sphere

TL;DR

This paper computes Wilson loop averages in large N Yang-Mills theory on a 2D sphere, revealing their dependence on Young tableau density and unifying results for different loop complexities across phases.

Contribution

It provides explicit formulas for Wilson loop averages in large N 2D Yang-Mills theory, connecting them to Young tableau densities and loop equations for self-intersecting loops.

Findings

Wilson loop averages expressed via Young tableau density

Results valid in both small and large sphere areas

Self-intersecting loop averages derived from simple loop results

Abstract

We calculate various Wilson loop averages in a pure $SU(N)$-gauge theory on a two-dimensional sphere, in the large $N$ limit. The results can be expressed through the density of rows in the most probable Young tableau. They are valid in both phases (small and large areas of the sphere). All averages for self-intersecting loops can be reproduced from the average for a simple (non self-intersecting) loop by means of loop equations.