Non-invertible symmetries in axion electrodynamics

TL;DR

This paper explores non-invertible symmetries in 3+1D axion electrodynamics, revealing new symmetry structures and their effects on extended objects like domain walls and flux tubes.

Contribution

It identifies a novel non-invertible 1-form symmetry in axion electrodynamics and analyzes its implications for extended objects and charge fractionalization.

Findings

Discovery of a non-invertible 1-form symmetry in axion electrodynamics

Correlation functions reveal induced fractional charges on domain walls

Fractional axionic operators appear at intersections of magnetic flux tubes

Abstract

We study non-invertible global symmetries in $(3+1)$-dimensional axion electrodynamics with a massless axion and a massless photon. In addition to a previously known non-invertible 0-form shift symmetry of the axion, we find a non-invertible 1-form symmetry associated with the equation of motion for the photon. Correlation functions of non-invertible symmetry defects lead to invertible 1- and 2-form symmetry defects associated with Bianchi identities for the axion and photon. In terms of the correlation functions, we discuss several phenomena for extended objects, such as induced fractional electric charges on axionic domain walls and fractional axionic operators on intersection points of magnetic flux tubes from the viewpoint of global symmetries.