Uniqueness of the minimum of the free energy of the 2D Yang-Mills theory at large N

TL;DR

This paper resolves a controversy in 2D Yang-Mills theory at large N by demonstrating that the free energy's minimum is unique when all relevant equations are considered, clarifying the theory's behavior.

Contribution

The paper identifies a missing equation in previous analyses, proving the uniqueness of the free energy minimum in 2D Yang-Mills theory at large N.

Findings

The minimum of the free energy is unique when the missing equation is included.

Clarification of the large N behavior of 2D Yang-Mills theories.

Resolution of previous controversies regarding multiple minima.

Abstract

There has been some controversies at the large $N$ behaviour of the 2D Yang-Mills and chiral 2D Yang-Mills theories. To be more specific, is there a one parameter family of minima of the free energy in the strong region, or the minimum is unique. We show that there is a missed equation which, added to the known equations, makes the minimum unique.