Induced parity-odd effective action for a Dirac field on S 2 × S 1

Abstract

We evaluate the parity-odd part of the effective action due to massive Dirac fermions on a S 2 × S 1 manifold, minimally coupled to an external Abelian gauge field. We do that for a special class of gauge-field configurations, which is especially suitable to the study of the behavior of the fermionic determinant under large gauge field configurations, which are allowed by the space-time geometry.