On gauging finite subgroups

Abstract

We study in general spacetime dimension the symmetry of the theory obtained by gauging a non-anomalous finite normal Abelian subgroup A of a Γ-symmetric theory. Depending on how anomalous Γ is, we find that the symmetry of the gauged theory can be i) a direct product of G = Γ/A and a higher-form symmetry  with a mixed anomaly, where  is the Pontryagin dual of A; ii) an extension of the ordinary symmetry group G by the higher-form symmetry Â; iii) or even more esoteric types of symmetries which are no longer groups. We also discuss the relations to the effect called the H3(G, Â) symmetry localization obstruction in the condensed-matter theory and to some of the constructions in the works of Kapustin-Thorngren and Wang-Wen-Witten.