Quantum Free Yang-Mills on the Plane

TL;DR

This paper develops a free-probability quantum Yang-Mills theory on the plane, computes Wilson loop expectations, and demonstrates it as the large N limit of traditional U(N) quantum Yang-Mills theory.

Contribution

It introduces a free-probability framework for quantum Yang-Mills theory on the plane and connects it to the classical large N limit.

Findings

Wilson loop expectations are explicitly determined.

The free theory is shown to be the N→∞ limit of U(N) quantum Yang-Mills.

Provides a new probabilistic approach to gauge theories.

Abstract

We construct a free-probability quantum Yang-Mills theory on the two dimensional plane, determine the Wilson loop expectation values, and show that this theory is the $N=\infty$ limit of U(N) quantum Yang-Mills theory on the plane.