Effect of Bare Mass on the Hosotani Mechanism

It is pointed out that the existence of bare mass terms for matter fields changes gauge symmetry patterns through the Hosotani mechanism. As a demonstration, we study an SU(2) gauge model with massive adjoint fermions defined on $M^4\otimes S^1$. It turns out that the vacuum structure changes at certain critical values of $mL$, where $m~(L)$ stands for the bare mass (the circumference of $S^1$). The gauge symmetry breaking patterns are different from models with massless adjoint fermions. We also consider a supersymmmetric SU(2) gauge model with adjoint hypermultiplets, in which the supersymmetry is broken by bare mass terms for the gaugino and squark fields instead of the Scherk-Schwarz mechanism.