Neutral Multi-Instanton as a Bridge from Weak to Strong Coupling phase in Two Dimensional QCD

TL;DR

This paper investigates the role of neutral multi-instantons in two-dimensional $U(N)$ Yang-Mills theory, demonstrating how they connect weak and strong coupling phases through analytical and numerical analysis.

Contribution

It introduces the neutral multi-instanton approximation as a key to understanding the phase transition in 2D Yang-Mills theory at large N.

Findings

Neutral multi-instantons dominate in the strong coupling region.

Numerical calculations match large N exact solutions.

Neutral multi-instantons bridge weak and strong coupling phases.

Abstract

Using a contour integral representation we analyze the multi-instanton sector in two dimensional $U(N)$ Yang-Mills theory on a sphere and argue the role of multi-instanton in the large $N$ phase transition. In the strong coupling region at the large $N$ , we encounter ``singular saddle point''. Because of this situation, ``neutral'' configurations of the multi-instanton are dominant in this region. Based on the ``neutral'' multi-instanton approximation we numerically calculate the multi-instanton amplitude , the free energies and the Wilson loops for finite $N$ . We also compare our results with the large $N$ exact solution of the free energy and the Wilson loop and argue some problems. We find the ``neutral'' multi-instanton contribution bridges the gap between weak and strong coupling phase.