Effects of Fermion Masses and Twisting on Non-Integrable Phases on Compact Extra Dimensions

The effective potential for the Wilson loop in the SU(2) gauge theory with N_f massive fundamental and N_a massive adjoint fermions on S^1 x M^4 is computed at the one-loop level, assuming periodic boundary conditions for the gauge field and general boundary conditions for fermions. It is shown that there are critical values for the bare mass, and the boundary condition parameter for the adjoint fermions, beyond which the symmetry pattern changes. However, neither bare mass, nor the boundary condition parameter for the fundamental fermion play any role on the vacuum structure, thus the symmetry breaking pattern. When the two different types of fermions with equal masses exist together the pattern of the fundamental fermion dominate, and SU(2) gauge symmetry remains intact independent of the fermion masses.