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

Understand

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.