Global 3-group symmetry and 't Hooft anomalies in axion electrodynamics

TL;DR

This paper explores the complex higher-group symmetry structure and 't Hooft anomalies in massless axion electrodynamics, revealing a novel cubic mixed anomaly specific to the higher-group framework.

Contribution

It demonstrates that the higher-form symmetries form a global semistrict 3-group and identifies a unique cubic mixed 't Hooft anomaly in the theory.

Findings

Higher-form symmetries form a 3-group structure

Identification of a cubic mixed 't Hooft anomaly

Reveals new anomaly specific to higher-group symmetries

Abstract

We investigate a higher-group structure of massless axion electrodynamics in $(3+1)$ dimensions. By using the background gauging method, we show that the higher-form symmetries necessarily have a global semistrict 3-group (2-crossed module) structure, and exhibit 't Hooft anomalies of the 3-group. In particular, we find a cubic mixed 't Hooft anomaly between 0-form and 1-form symmetries, which is specific to the higher-group structure.