Phase Transitions for Gauge Theories on Tori from the AdS/CFT Correspondence

TL;DR

This paper explores phase transitions in large-N gauge theories on tori using AdS/CFT correspondence, revealing how vacuum stress tensors and phase behavior depend on torus periodicities and finite N effects.

Contribution

It provides a detailed analysis of phase transitions in gauge theories on tori via AdS/CFT, including finite N corrections and a comparison with known finite-temperature transitions.

Findings

Vacuum stress tensor shows tension along smallest periodicity

Phase transition occurs when shortest periodicities cross

Finite N effects are approximated at zero-loop level

Abstract

The vacuum of a large-N gauge field on a p-torus has a spatial stress tensor with tension along the direction of smallest periodicity and equal pressures (but p times smaller in magnitude) along the other directions, assuming an AdS/CFT correspondence and a refined form of the Horowitz-Myers positive-energy conjecture. For infinite N, the vacuum exhibits a phase transition when the lengths of the two shortest periodicities cross. A comparison is made with the Surya-Schleich-Witt phase transition at finite temperature. A zero-loop approximation is also given for large but finite N.