The Phase Structure of Low Dimensional Large N Gauge Theories on Tori

TL;DR

This paper investigates the phase structure of large N gauge theories on tori, analyzing how various parameters influence their thermodynamics through analytical, numerical, and dual gravitational methods.

Contribution

It provides a comprehensive analysis of phase transitions in toroidally compactified large N gauge theories, including supersymmetric cases and massive adjoint fields.

Findings

Identified phase transition points depending on coupling and geometry.

Mapped phase diagrams for different gauge theories on tori.

Validated analytical results with Monte Carlo simulations.

Abstract

In this paper we continue our study of the thermodynamics of large N gauge theories on compact spaces. We consider toroidal compactifications of pure SU(N) Yang-Mills theories and of maximally supersymmetric Yang-Mills theories dimensionally reduced to 0+1 or 1+1 dimensions, and generalizations of such theories where the adjoint fields are massive. We describe the phase structure of these theories as a function of the gauge coupling, the geometry of the compact space and the mass parameters. In particular, we study the behavior of order parameters associated with the holonomy of the gauge field around the cycles of the torus. Our methods combine analytic analysis, numerical Monte Carlo simulations, and (in the maximally supersymmetric case) information from the dual gravitational theories.