Dynamical Gauge Symmetry Breaking and Mass Generation on the Orbifold T²/Z₂

Dynamical gauge symmetry breaking on the orbifold $T^2/Z_2$ is shown to occur through quantum dynamics of Wilson line phases. Different sets of boundary conditions on $T^2/Z_2$ can be related to each other by Wilson line phases, forming equivalence classes. The effective potential for Wilson line phases is evaluated at the one loop level in SU(2) gauge theory. Depending on the fermion content, the SU(2) symmetry can be broken either completely or partially to U(1) without introducing additional Higgs scalar fields. When SU(2) is completely broken, each of three components of the gauge fields may acquire a distinct mass. Masses are generated through the combination of $T^2$ twists and dynamics of Wilson line phases.