Phase structure and Hosotani mechanism in gauge theories with compact dimensions revisited

TL;DR

This paper explores the phase structure of SU(3) gauge theories with compact dimensions, revealing rich symmetry-breaking phases and their dependence on matter content and compactification size, supported by perturbative and lattice consistency.

Contribution

It provides a detailed analysis of gauge symmetry breaking and phase transitions in higher-dimensional gauge theories with various matter fields using effective potential methods.

Findings

Identification of multiple gauge-symmetry-broken phases including $SU(2)\times U(1)$ split and $U(1)\times U(1)$ re-confined phases.

Demonstration that adding fundamental quarks enhances the split phase and introduces a pseudo-reconfined phase.

Observation of gradual chiral symmetry restoration as the compact dimension shrinks.

Abstract

We investigate the phase structure of SU(3) gauge theory in four and five dimensions with one compact dimension by using perturbative one-loop and PNJL-model-based effective potentials, with emphasis on spontaneous gauge symmetry breaking. When adjoint matter with the periodic boundary condition is introduced, we have rich phase structure in the quark-mass and compact-size space with gauge-symmetry-broken phases, called the $SU(2)\times U(1)$ split and the $U(1)\times U(1)$ re-confined phases. Our result is qualitatively consistent with the recent lattice calculations. When fundamental quarks are introduced in addition to adjoint quarks, the split phase becomes more dominant and larger as a result of explicit center symmetry breaking. We also show that another $U(1)\times U(1)$ phase (pseudo-reconfined phase) with negative vacuum expectation value of Polyakov loop exists in this case. We study chiral properties in these theories and show that chiral condensate gradually decreases and chiral symmetry is slowly restored as the size of the compact dimension is decreased.