Higher-form symmetries and 3-group in axion electrodynamics

TL;DR

This paper explores the higher-form symmetries in axion electrodynamics, revealing a 3-group structure that explains phenomena like the Witten effect and anomalous Hall effect.

Contribution

It demonstrates that the higher-form symmetries in axion electrodynamics form a semistrict 3-group, providing a new mathematical framework for understanding related physical effects.

Findings

Higher-form symmetries form a 3-group structure.

Correlation functions reveal the 3-group structure.

Witten and anomalous Hall effects are described by 3-group transformations.

Abstract

We study higher-form symmetries in a low-energy effective theory of a massless axion coupled with a photon in $(3+1)$ dimensions. It is shown that the higher-form symmetries of this system are accompanied by a semistrict 3-group (2-crossed module) structure, which can be found by the correlation functions of symmetry generators of the higher-form symmetries. We argue that the Witten effect and anomalous Hall effect in the axion electrodynamics can be described in terms of 3-group transformations.