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

It is shown that the logarithmic derivative of the characteristic polynomial of a Wilson loop in two-dimensional pure Yang Mills theory with gauge group SU(N)SU(N) exactly satisfies Burgers' equation, with viscosity given by 1/(2N)1/(2N). The Wilson loop does not intersect itself and Euclidean space–time is assumed flat and infinite. This result provides a precise framework in 2D YM for recent observations of Blaizot and Nowak and was inspired by their work.