Eigenvalue density of Wilson loops in 2D SU(N) YM at large N

TL;DR

This paper investigates the eigenvalue density of Wilson loops in 2D SU(N) Yang-Mills theory at large N, revealing a phase transition and analyzing finite N effects through saddle-point methods.

Contribution

It provides a detailed analysis of eigenvalue densities and phase transitions in 2D SU(N) Yang-Mills theory, including finite N corrections and their relation to known infinite N results.

Findings

Eigenvalue density exhibits a phase transition at a critical loop size.

Finite N averages lead to smoothed expressions approximating the infinite N singularity.

Saddle-point analysis confirms convergence to known large N results.

Abstract

The eigenvalue density of a Wilson loop matrix W associated with a simple loop in two-dimensional Euclidean SU(N) Yang-Mills theory undergoes a phase transition at a critical size in the infinite-N limit. The averages of 1/det(z-W) and det(1+uW)/(1-vW) at finite N lead to two different smoothed out expressions. It is shown by a saddle-point analysis that both functions tend to the known singular result at infinite N.