We study in general spacetime dimension the symmetry of the theory
obtained by gauging a non-anomalous finite normal Abelian subgroup
AA
of a \GammaΓ-symmetric
theory. Depending on how anomalous \GammaΓ
is, we find that the symmetry of the gauged theory can be i) a direct
product of G=\Gamma/AG=Γ/A
and a higher-form symmetry \hat AÂ
with a mixed anomaly, where \hat AÂ
is the Pontryagin dual of AA;
ii) an extension of the ordinary symmetry group
GG
by the higher-form symmetry \hat AÂ;
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)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.
Correlations between Complexity and Entanglement in a One-Dimensional XY Model
