The Hosotani Mechanism in Bulk Gauge Theories with an Orbifold Extra Space S¹/Z₂

We pursue the possibility of the scenario in which the Higgs field is identified with the extra-space component of a bulk gauge field. The space-time we take is M$^{4}$ $\otimes$ S$^1$/Z$_2$. We show that a non-trivial Z$_2$-parity assignment allows some of the extra-space component to have radiatively induced VEV, which strongly modifies the mass spectrum and gauge symmetry of the theory, realized by oribifolding. In particular we investigate the dynamical mass generation of zero-mode fermion and spontaneous gauge symmetry breaking due to the VEV. The gauge theories we adopt are a prototype model SU(2) and SU(3) model, of special interest as the realistic minimal scheme to incorporate the standard model SU(2) $\times$ U(1).