Symmetry extension by condensation defects II: general dimensions and higher-groups

Abstract

We discuss a class of symmetry structures in general spacetime dimension that arise when gauging symmetries in theories with a cubic 't Hooft anomaly. The anomaly mixes two Abelian discrete symmetries $A$ and $B$ with a characteristic class for an additional symmetry $C$, and we gauge $A\times B$. The novelty of this construction is that the resulting symmetry structure involves certain condensation defects of the dual symmetry $\hat{A}\times \hat{B}$. Specifically, these defects generate an invertible symmetry that extends $C$, either as an ordinary group extension or as a higher-group, depending on the characteristic class. We describe the corresponding charged operators and states, and illustrate the mechanism in several examples.

37 pages + appendices, 22 figures, 1 table. v2: typos corrected, references and acknowledgments added