On gauging finite subgroups
We study in general spacetime dimension the symmetry of the theory obtained by gauging a non-anomalous finite normal Abelian subgroup A A of a \Gamma Γ -symmetric theory. Depending on how anomalous \Gamma Γ is, we find that the symmetry of the gauged theory can be i) a direct product of G=\Gamma/A G...
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| Published in | SciPost physics Vol. 8; no. 1; p. 015 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
SciPost
01.01.2020
|
| Online Access | Get full text |
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| Summary: | We study in general spacetime dimension the symmetry of the theory
obtained by gauging a non-anomalous finite normal Abelian subgroup
A
A
of a
\Gamma
Γ
-symmetric
theory. Depending on how anomalous
\Gamma
Γ
is, we find that the symmetry of the gauged theory can be i) a direct
product of
G=\Gamma/A
G
=
Γ
/
A
and a higher-form symmetry
\hat A
A
̂
with a mixed anomaly, where
\hat A
A
̂
is the Pontryagin dual of
A
A
;
ii) an extension of the ordinary symmetry group
G
G
by the higher-form symmetry
\hat A
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)
H
3
(
G
,
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. |
|---|---|
| ISSN: | 2542-4653 2542-4653 |
| DOI: | 10.21468/SciPostPhys.8.1.015 |