High Temperature Confinement in SU(N) Gauge Theories

TL;DR

This paper explores high-temperature confinement in SU(N) gauge theories with adjoint fermions, combining lattice simulations and semiclassical analysis to understand the phase structure and string tensions.

Contribution

It provides a detailed analysis of high-temperature confinement mechanisms and predicts calculable string tensions, connecting lattice results with semiclassical theory.

Findings

Confinement persists at high temperature with light adjoint fermions.

Polyakov loop potential exhibits Z(N) symmetry in the confining phase.

String tensions vary smoothly with fermion mass to temperature ratio.

Abstract

SU(N) gauge theories, extended with adjoint fermions having periodic boundary conditions, are confining at high temperature for sufficiently light fermion mass m. Lattice simulations indicate that this confining region is smoothly connected to the confining region of low-temperature pure SU(N) gauge theory. In the high temperature confining region, the one-loop effective potential for Polyakov loops has a Z(N)-symmetric confining minimum. String tensions associated with Polyakov loops are smooth functions of m/T. In the magnetic sector, the Polyakov loop plays a role similar to a Higgs field, leading to a breaking of SU(N) to U(1)^{N-1}. This is turn yields an effective theory where magnetic monopoles give rise to string tensions for spatial Wilson loops. These string tensions are calculable semiclassically. There are many analytical predictions for the high-temperature region that can be tested by lattice simulations, but lattice work will be crucial for exploring the crossover from this region to the low-temperature confining behavior of pure gauge theories.