Dynamical gauge symmetry breaking and mass generation on the orbifold T**2 / Z(2)

Dynamical gauge symmetry breaking on the orbifold ${T}^{2}{/Z}_{2}$ is shown to occur through the 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 $\mathrm{SU}(2)$ gauge theory. Depending on the fermion content, the $\mathrm{SU}(2)$ symmetry can be broken either completely or partially to $U(1)$ without introducing additional Higgs scalar fields. When $\mathrm{SU}(2)$ 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.