The Master Field For 2D QCD On The Sphere

TL;DR

This paper derives an explicit master field for 2D QCD on the sphere in the large N limit, providing a new analytical tool for understanding gauge field correlations in a topological gauge setting.

Contribution

It introduces a novel explicit master field for the field strength and gauge potential in 2D QCD on the sphere, advancing the analytical understanding of gauge theories in the large N limit.

Findings

Explicit master field for field strength on the sphere

Master field for gauge potential consistent with field strength

Analytical expressions for field correlators in 2D QCD

Abstract

We continue our analysis of the field strength correlation functions of two-dimensional QCD on Riemann surfaces by studying the large $N$ limit of these correlation functions on the sphere for gauge group $U(N)$. Our results allow us to exhibit an explicit master field for the field strength $F_{\mu\nu}$ in a ``topological gauge'', given by a single master matrix in the Lie algebra of the maximal torus of the gauge group. Field correlators are obtained from traces of products of the master field. We also obtain a master field for the gauge potential $A_{\mu}$ on the sphere, consistent with the master field for the field strength.