Gauging discrete symmetries

Abstract

Recent developments in quantum gravity theory have led to the suggestion that various discrete symmetries, in particular charge–parity (CP), should be ‘‘gauged,’’ that is, interpreted as elements of some connected Lie group. As the parity operator is related to a space–time isometry, however, it is far from clear that this suggestion has any real meaning. We give a simple geometric construction in terms of which it is meaningful to ‘‘gauge’’ discrete symmetries, provided that certain nontrivial conditions are satisfied by the space–time manifold, by the gauge group, and by the discrete symmetry itself.