Instanton Induced Large $N$ Phase Transitions in Two and Four Dimensional QCD

TL;DR

This paper investigates how instantons induce large N phase transitions in two-dimensional QCD and explores the potential for similar phenomena in four-dimensional QCD, providing new insights into non-perturbative effects.

Contribution

It constructs the 1/N expansion for 2D QCD, demonstrates instanton-induced phase transitions, and explores analogous effects in 4D QCD.

Findings

Phase transition from weak to strong coupling in 2D QCD is instanton-induced.

A double scaling limit at the transition point is established with string susceptibility $\

-1\

Abstract

The $1/N$ expansion of the weak coupling phase of two-dimensional QCD on a sphere is constructed. It is demonstrated that the phase transition from the weak to the strong coupling phase is induced by instantons. A double scaling limit of the theory at the point of the phase transition is constructed, the value of string susceptibility is determined to be $\gamma_{str}=-1$. The possibility of instanton induced large $N$ phase transitions in four dimensional QCD is explored.