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

TL;DR

This paper investigates the large N limit of Wilson loops in 2D Euclidean Yang-Mills theory on compact surfaces, establishing convergence on the torus and proposing a conjecture for other surfaces supported by partial results.

Contribution

It extends the understanding of the large N limit of Wilson loops to all orientable compact surfaces of genus ≥ 1, including the torus, and introduces the Makeenko-Migdal equations in this context.

Findings

Convergence of Wilson loops on the torus in the large N limit

Partial results supporting the conjecture for other surfaces

Formulation of Makeenko-Migdal equations for these surfaces

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.