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

TL;DR

The paper demonstrates that massless axion electrodynamics in 3+1 dimensions hosts a semistrict 3-group of higher-form symmetries. By performing background gauging, it identifies three 't Hooft anomalies, including a cubic 2-group obstruction to simultaneously gauging 0-form and 1-form symmetries. It presents two compatible gauging routes—a direct background-gauging approach and a 3-group gauge theory formulation—and shows their equivalence, thereby providing a coherent 3-group framework for the theory. The findings constrain potential gapped phases and offer a robust platform for analyzing axion-related topological phenomena in nontrivial backgrounds and on axionic domain walls.

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.