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On gauging finite subgroups

Yuji Tachikawa

SciPost Phys. 8, 015 (2020) · published 31 January 2020

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 ˆA with a mixed anomaly, where ˆA is the Pontryagin dual of A; ii) an extension of the ordinary symmetry group G by the higher-form symmetry ˆA; 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,ˆA) symmetry localization obstruction in the condensed-matter theory and to some of the constructions in the works of Kapustin-Thorngren and Wang-Wen-Witten.

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Abelian symmetries Gauge theory

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