Complex Burgers' equation in 2D SU(N) YM

TL;DR

This paper derives an integro-differential equation for eigenvalue density in 2D SU(N) Yang Mills theory, extending the infinite N solution to finite N using complex Burgers' equations with viscosity.

Contribution

It introduces a novel integro-differential equation for eigenvalue density in 2D SU(N) YM, connecting complex Burgers' equations to finite N extensions of known solutions.

Findings

Derived an eigenvalue density equation from complex Burgers' equations.

Extended the Durhuus and Olesen infinite N solution to finite N.

Provided a non-unique finite N extension of the solution.

Abstract

An integro-differential equation satisfied by an eigenvalue density defined as the logarithmic derivative of the average inverse characteristic polynomial of a Wilson loop in two dimensional pure Yang Mills theory with gauge group SU(N) is derived from two associated complex Burgers' equations, with viscosity given by 1/(2N). The Wilson loop does not intersect itself and Euclidean space-time is assumed flat and infinite. This result provides an extension of the infinite N solution of Durhuus and Olesen to finite N, but this extension is not unique.