The equation of state of two dimensional Yang-Mills theory

TL;DR

This paper investigates the equation of state of two-dimensional SU(N) gauge theory, revealing a scale-dependent crossover that becomes a first-order transition at large N, with implications for understanding gauge theories on compact spaces.

Contribution

It provides a detailed analysis of the pressure behavior and phase transition nature of 2D Yang-Mills theory on a torus as N varies.

Findings

Identification of a crossover scale separating large and small circle regimes

The crossover scale approaches zero as N increases

The transition becomes first order in the large N limit

Abstract

We study the pressure, $P$, of SU($N$) gauge theory on a two-dimensional torus as a function of area, $A=l/t$. We find a cross-over scale that separates the system on a large circle from a system on a small circle at any finite temperature. The cross-over scale approaches zero with increasing $N$ and the cross-over becomes a first order transition as $N\to\infty$ and $l\to 0$ with the limiting value of $2Pl/(N-1)t$ depending on the fixed value of $Nl$.