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.
TY - JOUR
PB - SciPost Foundation
DO - 10.21468/SciPostPhys.8.1.015
TI - On gauging finite subgroups
PY - 2020/01/31
UR - https://scipost.org/SciPostPhys.8.1.015
JF - SciPost Physics
JA - SciPost Phys.
VL - 8
IS - 1
SP - 015
A1 - Tachikawa, Yuji
AB - 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.
ER -@Article{10.21468/SciPostPhys.8.1.015,
title={{On gauging finite subgroups}},
author={Yuji Tachikawa},
journal={SciPost Phys.},
volume={8},
pages={015},
year={2020},
publisher={SciPost},
doi={10.21468/SciPostPhys.8.1.015},
url={https://scipost.org/10.21468/SciPostPhys.8.1.015},
}
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