Recurrent dynamical symmetry breaking and restoration by Wilson lines at finite densities on a torus

TL;DR

This paper derives the one-loop effective potential for Wilson lines in an SU(N) gauge theory with adjoint fermions on a torus, revealing that gauge symmetry undergoes alternating breaking and restoration as fermion density varies.

Contribution

It provides a general expression for the effective potential at finite density and temperature, and uncovers a novel quantum effect of symmetry oscillation driven by nonintegrable phases.

Findings

Gauge symmetry breaks and restores alternately with increasing fermion density.

The phase structure is explicitly characterized for SU(2) at zero temperature.

Quantum effects of nonintegrable phases cause symmetry oscillations.

Abstract

In this paper we derive the general expression of a one-loop effective potential of the nonintegrable phases of Wilson lines for an SU(N) gauge theory with a massless adjoint fermion defined on the spactime manifold $R^{1,d-3}\times T^2$ at finite temperature and fermion density. The Phase structure of the vacuum is presented for the case with $d=4$ and N=2 at zero temperature. It is found that gauge symmetry is broken and restored alternately as the fermion density increases, a feature not found in the Higgs mechanism. It is the manifestation of the quantum effects of the nonintegrable phases.