2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/211528An 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.10 pages; fixed typo in eq. 37, updated 1 reference and added 2 minor clarifying commentsHigh Energy Physics - TheoryHigh Energy Physics - LatticeMathematical Physicstext