Selection rules of topological solitons from non-invertible symmetries in axion electrodynamics

TL;DR

This paper explores how non-invertible symmetries impose selection rules on topological solitons like axionic domain walls and magnetic strings in 3+1D axion electrodynamics, providing new insights into soliton configurations and the axionic domain wall problem.

Contribution

It identifies non-invertible symmetry generators as topological solitons and derives new constraints on their configurations, advancing understanding of symmetry and soliton interactions in axion electrodynamics.

Findings

Non-invertible symmetries correspond to axionic domain walls and magnetic strings.

Constraints on soliton configurations in the presence of monopoles and strings.

A solution to the axionic domain wall problem involving magnetic monopoles.

Abstract

We investigate a relation between non-invertible symmetries and selection rules of topological solitons such as axionic domain walls and magnetic strings in the $(3+1)$-dimensional axion electrodynamics with a massive axion or a massive photon. In the low-energy limit of the phases where either the axion or the photon is massive, we identify non-invertible 0- or 1-form symmetry generators as axionic domain walls or magnetic strings, respectively. By non-invertible transformations on magnetic monopoles or axionic strings, we give constraints on possible configurations of topological solitons in the presence of the monopoles or axionic strings. Our results are consistent with a solution to the axionic domain wall problem by the magnetic monopole. Further, we give a new constraint on a linked configuration of the magnetic and axionic strings.