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

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.