The formulation of gauge-Higgs unification with dynamical boundary conditions

Abstract

The boundary conditions on multiply connected extra dimensions play major rolls 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 M^4 times S^1/Z_2. 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 $SU(5)$ gauge group, sets of boundary conditions which lead to SU(5) to SU(3) times SU(2) times U(1) symmetry breaking are naturally included in the restricted sets.