Effective theory of vortices in two-dimensional spinless chiral p -wave superfluids

We propose a U(1)×Z2 effective gauge theory for vortices in a px+ipy superfluid in two dimensions. The combined gauge transformation binds U(1) and Z2 defects so that the total transformation remains single-valued and manifestly preserves the particle-hole symmetry of the action. The Z2 gauge field introduces a complete Chern-Simons term in addition to a partial one associated with the U(1) gauge field. The theory reproduces the known physics of vortex dynamics such as a Magnus force proportional to the superfluid density. More importantly, it predicts a universal Abelian phase, exp(iπ/8), upon the exchange of two vortices. This phase is modified by nonuniversal corrections due to the partial Chern-Simon term, which are nevertheless screened in a charged superfluid at distances that are larger than the penetration depth.