Degenerate Fermions and Wilson Loop in $1+1$ Dimensions

TL;DR

This paper studies how finite fermion density influences symmetry breaking and restoration via Wilson loops in 1+1 dimensional models with SU(2) and SU(3) gauge symmetries, revealing density-driven phase transitions independent of boundary conditions.

Contribution

It demonstrates that symmetry transitions driven by fermion density occur in 1+1D gauge models regardless of boundary conditions, contrasting with temperature-driven transitions.

Findings

Symmetry breaking and restoration depend on fermion density.

Transitions occur at finite density, independent of boundary conditions.

Contrasts with temperature-driven phase transitions in previous studies.

Abstract

We investigate the effect of finite fermion density on symmetry breaking by Wilson loops in $(1+1)$ dimensions. We find the breaking and restoration of symmetry at finite density in the models with $SU(2)$ and $SU(3)$ gauge symmetries, in the presence of the adjoint fermions. The transition can occur at a finite density of fermions, regardless of the periodic or antiperiodic boundary condition of the fermion field; this is in contrast to the finite-temperature ease examined by Ho and Hosotani (Nucl. Phys. B345 (1990) 445) where the boundary condition of fractional twist is essential to the occurrence of the phase transition.