Models with rank-reducing discrete boundary conditions on T²/ℤ₄

We study six-dimensional SU(n) gauge models with rank-reducing discrete boundary conditions on the orbifold T²/ℤ₄, without and with continuous Wilson line phases. For the latter case, we find that a minimal model can describe the breakdown of the electroweak symmetry based on an SU(6) gauge group. This model possesses excellent features that two Higgs doublets come from the zero modes of the extra-dimensional gauge field, and the quarks in each generation can be unified into one multiplet, without exotic quarks, as the zero modes of a bulk field in the 15 representation of SU(6). There exists a vacuum where the electroweak symmetry is slightly broken by the Hosotani mechanism, with the addition of suitable bulk fields. Interestingly, quadratic divergences are not reintroduced into the Higgs masses from the tadpole terms of the field strength localized on fixed points, not only at one-loop level but also at higher orders.