Large-N limit of the generalized 2-dimensional Yang-Mills theories

TL;DR

This paper analyzes the large-N limit of generalized 2D Yang-Mills theories, deriving explicit relations for free energy in weak coupling and revealing a third order phase transition in the strong coupling regime.

Contribution

It provides an explicit saddle-point analysis for the large-N limit and uncovers a new equation governing the strong coupling phase of the fourth Casimir theory.

Findings

Explicit relation for free energy in weak region

Identification of a third order phase transition

New equation governing the strong coupling phase

Abstract

Using the standard saddle-point method, we find an explicit relation for the large-N limit of the free energy of an arbitrary generalized 2D Yang-Mills theory in the weak ($A<A_c$) region. In the strong ($A>A_c$) region, we investigate carefully the specific fourth Casimir theory, and show that the ordinary integral equation of the density function is not adequate to find the solution. There exist, however, another equation which restricts the parameters. So one can find the free energy in strong region and show that the theory has a third order phase transition.