Large $N$ behaviour of the two-dimensional Yang-Mills partition function

Abstract

We compute the large N limit of the partition function of the Euclidean Yang--Mills measure with structure group SU(N) or U(N) on all closed compact surfaces, orientable or not, excepted for the sphere and the projective plane. This limit is finite as opposed to the case of the sphere and presumably the projective plane. We expect that the results we present might give an insight towards the master field on these surfaces.