VORTEX DYNAMICS IN SELF-DUAL CHERN-SIMONS-HIGGS SYSTEMS

We consider vortex dynamics in self-dual Chern-Simons-Higgs systems. We show that the naive Aharonov-Bohm phase is the inverse of the statistical phase expected from the vortex spin, and that the self-dual configurations of vortices are degenerate in energy but not in angular momentum. We also use the path integral formalism to derive the dual formulation of Chern-Simons-Higgs systems in which vortices appear as charged particles. We argue that in addition to the electromagnetic interaction, there is an additional interaction between vortices, the so-called Magnus force, and that these forces can be put together into a single ''dual electromagnetic'' interaction. This dual electromagnetic interaction leads to the right statistical phase. We also derive and study the effective action for slowly moving vortices, which contains terms both linear and quadratic in the vortex velocity. We show that vortices can be bounded to each other by the Magnus force.