Large N limit of the Yang-Mills measure on compact surfaces II: Makeenko-Migdal equations and planar master field

Abstract: This paper considers the large N limit of Wilson loops for the two-dimensional Euclidean Yang-Mills measure on all orientable compact surfaces of genus larger or equal to one, with a structure group given by a classical compact matrix Lie group. We show their convergence for all loops on the torus and give a conjecture supported by partial results for other surfaces.