Vortex Dynamics in Self-Dual Chern-Simons Higgs Systems

TL;DR

This paper investigates vortex dynamics in self-dual Chern-Simons Higgs systems, revealing the dual nature of vortex interactions, the role of the Magnus force, and deriving an effective action for slow vortex motion.

Contribution

It introduces a dual formulation where vortices are charged particles and clarifies the interactions, including the Magnus force, affecting vortex statistics and dynamics.

Findings

Naive Aharanov-Bohm phase is inverse of expected statistical phase

Self-dual vortices are degenerate in energy but not in angular momentum

Derived effective action for slow vortex motion with velocity-dependent terms

Abstract

We consider vortex dynamics in self-dual Chern-Simons Higgs systems. We show that the naive Aharanov-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 besides 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 Aharanov-Bohm phase. We also derive and study the effective action for slowly moving vortices, which contains terms both linear and quadratic in the vortex velocity.