Black hole-black string phase transitions in thermal 1+1-dimensional supersymmetric Yang-Mills theory on a circle

TL;DR

This paper investigates the phase transition between black hole and black string configurations in a 1+1-dimensional supersymmetric Yang-Mills theory, using both gravity calculations and Monte Carlo simulations to analyze the transition at different couplings.

Contribution

It extends previous work by providing a detailed phase diagram and evidence of a similar phase transition in the weakly coupled gauge theory, supported by Monte Carlo methods and a Landau-Ginzburg model.

Findings

Strong evidence of black hole-black string phase transition at weak coupling.

The phase transition is near the boundary between first and second order.

A Landau-Ginzburg model effectively describes the transition behavior.

Abstract

We review and extend earlier work that uses the AdS/CFT correspondence to relate the black hole-black string transition of gravitational theories on a circle to a phase transition in maximally supersymmetric 1+1-dimensional SU(N) gauge theories at large N, again compactified on a circle. We perform gravity calculations to determine a likely phase diagram for the strongly coupled gauge theory. We then directly study the phase structure of the same gauge theory, now at weak 't Hooft coupling. In the interesting temperature regime for the phase transition, we may reduce the 1+1-dimensional theory to a 0+1-dimensional bosonic theory, which we solve using Monte Carlo methods. We find strong evidence that the weakly coupled gauge theory also exhibits a black hole-black string like phase transition in the large N limit. We demonstrate that a simple Landau-Ginzburg like model describes the behaviour near the phase transition remarkably well. The weak coupling transition appears to be close to the cusp between a first order and a second order transition.