Thermodynamics of large-$N$ gauge theories on a sphere: weak versus strong coupling

TL;DR

This paper investigates the thermodynamics of large-N gauge theories on a sphere, revealing novel weak-coupling behaviors and universal corrections, and discusses potential phase transitions between weak and strong coupling regimes.

Contribution

It extends the analysis of thermodynamic corrections from strong to weak coupling in large-N gauge theories on a sphere, uncovering new eigenvalue distribution effects and universal terms.

Findings

Deviation of Polyakov loop from one starts at 1/T^3

Universal T/4 term in free energy

Eigenvalue distribution non-uniformity affects thermodynamics

Abstract

Recently lattice simulation in pure Yang-Mills theory exposes significant quadratic corrections for both the thermodynamic quantities and the renormalized Polyakov loop in the deconfined phase. These terms are previously found to appear naturally for ${\mathcal N}=4$ Super Yang-Mills~(SYM) on a sphere at strong coupling, through the gauge/gravity duality. Here we extend the investigation to the weak coupling regime, and for general large-$N$ gauge theories. Employing the matrix model description, we find some novel behavior in the deconfined phase, which is not noticed in the literature. Due to the non-uniform eigenvalue distribution of the holonomy around the time circle, the deviation of the Polyakov loop from one starts from $1/T^3$ instead of $1/T^2$. Such a power is fixed by the space dimension and do not change with different theories. This statement is also true when perturbative corrections to the single-particle partition functions are included. The corrections to the Polyakov loop and higher moments of the distribution function combine to give a universal term, $T/4$, in the free energy. These differences between the weak and strong coupling regime could be easily explained if a strong/weak coupling phase transition occurs in the deconfined phase of large-$N$ gauge theories on a compact manifold.