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

TL;DR

This paper investigates the complex higher-form symmetries and 't Hooft anomalies in a topological phase of axion electrodynamics, revealing a semi-strict 4-group structure and its physical implications.

Contribution

It identifies a semi-strict 4-group structure in the higher-form symmetries of topological axion electrodynamics and analyzes associated 't Hooft anomalies.

Findings

Higher-form symmetries form a semi-strict 4-group structure.

Possible 't Hooft anomalies for the 4-group symmetry are identified.

Discussion of physical consequences of these anomalies.

Abstract

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.