Congruency class effects in the Hosotani model

Abstract

We examine the Wilson loop breaking of gauge and central symmetries by determining the background gauge field which minimises the one-loop effective potential for massless Dirac fermions on manifolds of the formR m × S 1 . By writing the effective potential in terms of the polylogarithm function, it is found that the algebra preserving minima are always turning points of the potential and that the positions of the global minima of the potential are independent of the dimension of the space. A condition is obtained for stability of the classical symmetric vacua with respect to radiative corrections. We find that the gauge algebra can only be broken if we have periodic fermions in a representation of the group which lies in the same congruency class as the adjoint representation. The degree of breaking of the covering group central symmetries is found to depend both on the choice of congruency class and boundary condition for the fermion fields.