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

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 12N. 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.