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

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 ${R}^{1,d\ensuremath{-}3}\ifmmode\times\else\texttimes\fi{}{T}^{2}$ 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.