Dynamical Rearrangement of Gauge Symmetry on the Orbifold S^1/Z_2

Gauge theory defined on the orbifold $M^4 \times (S^1/Z_2)$ is investigated from the viewpoint of the Hosotani mechanism. Rearrangement of gauge symmetry takes place due to the dynamics of Wilson line phases. The physical symmetry of the theory, in general, differs from the symmetry of the boundary conditions. Several sets of boundary conditions having distinct symmetry can be related by gauge transformations, belonging to the same equivalence class. The Hosotani mechanism guarantees the same physics in all theories in one equivalent class. Examples are presented in the SU(5) theory. Zero modes of the extra-dimensional components, $A_y$, of gauge fields acquire masses by radiative corrections. In the nonsupersymmetric SU(5) model the presence of bulk fermions leads to the spontaneous breaking of color SU(3). In the supersymmetric model with Scherk-Schwarz SUSY breaking zero modes of $A_y$'s acquire masses of order of the SUSY breaking.