Topological axion electrodynamics and 4-group symmetry

TL;DR

This paper explores the topological and symmetry properties of a low-energy effective theory of axion electrodynamics, revealing a 4-group structure and topologically ordered domain walls.

Contribution

It introduces a topological field theory for axion electrodynamics with higher-form symmetries and identifies a 4-group as the mathematical framework.

Findings

Existence of induced anyons on symmetry intersections

Topologically ordered axionic domain walls

Identification of a 4-group structure underlying the theory

Abstract

We study higher-form symmetries and a higher group in the low energy limit of a $(3+1)$-dimensional axion electrodynamics with a massive axion and a massive photon. A topological field theory describing topological excitations with the axion-photon coupling, which we call a topological axion electrodynamics, is obtained in the low energy limit. Higher-form symmetries of the topological axion electrodynamics are specified by equations of motion and Bianchi identities. We find that there are induced anyons on the intersections of symmetry generators. By a link of worldlines of the anyons, we show that the worldvolume of an axionic domain wall is topologically ordered. We further specify the underlying mathematical structure elegantly describing all salient features of the theory to be a 4-group.