Multi-Instanton Effect in Two Dimensional QCD

TL;DR

This paper investigates multi-instanton effects in two-dimensional U(N) Yang-Mills theory on a sphere, revealing their significant role in the large N phase transition through analytical and numerical methods.

Contribution

It introduces a contour integral representation for multi-instanton amplitudes and demonstrates the dominance of neutral configurations in the large N limit.

Findings

Neutral multi-instanton configurations dominate at large N

Multi-instanton interactions significantly influence the phase transition

Numerical calculations for N=3,4,5 support the analytical results

Abstract

We analyze multi-instanton sector in two dimensional U(N) Yang-Mills theory on a sphere. We obtain a contour intregrals representation of the multi-instanton amplitude and find ``neutral'' configurations of the even number instantons are dominant in the large N limit. Using this representation, we calculate 1,2,3,4 bodies interactions and the free energies for $N =3,4,5$ numerically and find that in fact the multi-instanton interaction effect essentially contribute to the large N phase transition discovered by Douglas and Kazakov.