The formulation of gauge-Higgs unification with dynamical boundary conditions

The boundary conditions on multiply connected extra dimensions play major roles in gauge-Higgs unification theory. Different boundary conditions, having been given in ad hoc manner so far, lead to different theories. To solve this arbitrariness problem of boundary conditions, we construct a formulation of gauge-Higgs unification with dynamics of boundary conditions on M4×S1/Z2M4×S1/Z2. As a result, it is found that only highly restricted sets of boundary conditions, which lead to nontrivial symmetry breaking, practically contribute to the partition function. In particular, we show that for SU(5)SU(5) gauge group, sets of boundary conditions which lead to SU(5)→SU(3)×SU(2)×U(1)SU(5)→SU(3)×SU(2)×U(1) symmetry breaking are naturally included in the restricted sets.