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

TL;DR

This paper analyzes the large N limit of the 2D Yang-Mills partition function on various surfaces, revealing finite limits except for the sphere and projective plane, which may inform the understanding of the master field.

Contribution

It provides the first detailed computation of the large N limit of 2D Yang-Mills on all closed surfaces except sphere and projective plane, highlighting their finite behavior.

Findings

Large N limit is finite for all surfaces except sphere and projective plane.

Results may offer insights into the master field on these surfaces.

Provides a comprehensive analysis across different topologies.

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.