Mapping of a thin-film ferromagnet to electrodynamics: quantum statistics of vortices

We consider a field-theoretic description of a thin-film ferromagnet with easy-plane anisotropy. The system can be mapped to the electrodynamics theory in (2+1)-dimensional space-time. The low-energy description is the familiar Maxwell electrodynamics. Spin waves become electromagnetic waves, whereas vortices turn into particles whose electric charge equals the vortex number n. A careful analysis of the high-energy theory reveals that these particles also carry a magnetic flux equal to the net spin of the vortex core S_z. Braiding two identical vortices yields an Aharonov-Bohm phase exp(2π i n S_z), which may lead to a nontrivial quantum statistics of vortices.