2017/12/31 by Yuji Tachikawa
Physics and Astronomy · #hep-th #cond-mat.str-el
paper · pdf · doi:10.21468/scipostphys.8.1.015
published as SciPost Phys. 8, 015 (2020) · 26 pages; v3: numerous minor improvements suggested by an anonymous referee; v2: minor improvement in Sec. 2.6.1
arxiv created 2019/12/23 · arxiv updated 2020/02/05
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 A with a mixed anomaly, where A is the Pontryagin dual of A; ii) an extension of the ordinary symmetry group G by the higher-form symmetry A; 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, 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.