SciPost Physics

On gauging finite subgroups

Yuji Tachikawa

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

• doi: 10.21468/SciPostPhys.8.1.015
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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 $\Gamma$-symmetric theory. Depending on how anomalous $\Gamma$ is, we find that the symmetry of the gauged theory can be i) a direct product of $G=\Gamma/A$ and a higher-form symmetry $\hat A$ with a mixed anomaly, where $\hat A$ is the Pontryagin dual of $A$; ii) an extension of the ordinary symmetry group $G$ by the higher-form symmetry $\hat A$; iii) or even more esoteric types of symmetries which are no longer groups. We also discuss the relations to the effect called the $H^3(G,\hat A)$ symmetry localization obstruction in the condensed-matter theory and to some of the constructions in the works of Kapustin-Thorngren and Wang-Wen-Witten.

• Daniel Robbins et al., Orbifolds from modular orbits
  Phys. Rev. D 101, 106021 (2020) [Crossref]
• Oren Bergman et al., Generalized symmetries and holography in ABJM-type theories
  J. High Energ. Phys. 2020, 77 (2020) [Crossref]
• Yuya Tanizaki et al., Modified instanton sum in QCD and higher-groups
  J. High Energ. Phys. 2020, 123 (2020) [Crossref]
• J.P. Ang et al., Line operators of gauge theories on non-spin manifolds
  J. High Energ. Phys. 2020, 87 (2020) [Crossref]
• Ryan Thorngren, Topological quantum field theory, symmetry breaking, and finite gauge theory in 3+1D
  Phys. Rev. B 101, 245160 (2020) [Crossref]
• Po-Shen Hsin et al., Symmetry-enriched quantum spin liquids in (3 + 1)d
  J. High Energ. Phys. 2020, 22 (2020) [Crossref]