The Roberge-Weiss transition and 't Hooft loops

TL;DR

This paper investigates the properties of 't Hooft loops and phase transitions in SU(N) gauge theories at high temperature with imaginary chemical potential, revealing their behavior and phase diagram features.

Contribution

It demonstrates that 't Hooft loops are well-defined at phase boundaries with dynamical quarks and explores their scaling and relation to interface tension at high temperature.

Findings

't Hooft loops satisfy Casimir scaling in pure glue theory

Phase diagram shows intersecting lines of first order transitions

Interface tension relates to 't Hooft loop at high temperature

Abstract

Roberge and Weiss showed that for SU(N) gauge theories, phase transitions occur in the presence of an imaginary quark chemical potential. We show that at asymptotically high temperature, where the phase transition is of first order, that even with dynamical quarks 't Hooft loops of arbitrary Z(N) charge are well defined at the phase boundary. To leading order in weak coupling, the 't Hooft loop satisfies Casimir scaling in the pure glue theory, but not with quarks. Because the chemical potential is imaginary, typically the interaction measure is negative on one side of the phase transition. Using a matrix model to model the deconfining phase transition, we compute the phase diagram for heavy quarks, in the plane of temperature and imaginary chemical potential. In general we find intersecting lines of first order transitions. Using a modified Polyakov loop which is Roberge-Weiss symmetric, we suggest that the interface tension is related to the 't Hooft loop only at high temperature, where the imaginary part of this Polyakov loop, and not the real part, is discontinuous across the phase boundary.