Global 4-group symmetry and 't Hooft anomalies in topological axion electrodynamics

We study higher-form global symmetries and a higher-group structure of a low-energy limit of (3 + 1)-dimensional axion electrodynamics in a gapped phase described by a topological action. We argue that the higher-form symmetries should have a semi-strict 4-group (3-crossed module) structure by consistency conditions of couplings of the topological action to background gauge fields for the higher-form symmetries. We find possible 't Hooft anomalies for the 4-group global symmetry, and discuss physical consequences.

Automated summary

In this study, we investigate the higher-form global symmetries and higher-group structure of a low-energy limit of (3 + 1)-dimensional axion electrodynamics, which is described by a topological action. We argue that the higher-form symmetries should have a semi-strict 4-group structure based on the consistency conditions of the topological action with background gauge fields. We also identify possible 't Hooft anomalies for the 4-group global symmetry and discuss their physical consequences.