Non-invertible symmetries in axion electrodynamics

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.