Large N limit of Wilson Loops on orientable closed surfaces in the light of Koike-Schur-Weyl duality and Spin Networks

TL;DR

This paper proves the convergence of Wilson loops in large N limits on orientable surfaces, using advanced duality and network techniques to refine existing methods in Yang-Mills theory.

Contribution

It introduces a refined approach employing Koike-Schur-Weyl duality and Spin Networks to analyze Wilson loops in the large N limit on complex surfaces.

Findings

Wilson loops converge in probability for large unitary groups

Refined methods improve understanding of Yang-Mills measures

Applicable to surfaces of genus greater than two

Abstract

We prove the convergence in probability of Wilson loops under the Yang-Mills measure on any closed, orientable surface of genus larger than two, for large unitary or special unitary groups. Our approach revisits and refines recent arguments for average Wilson loops under the Atiyah-Bott-Goldman measure and for the Yang-Mills measure, using Koike-Schur-Weyl duality and Spin Networks.