Low energy dynamics of U(1)^{N} Chern-Simons solitons

TL;DR

This paper studies the low energy behavior of vortices in a U(1)^N Chern-Simons model, revealing their interactions, bound states, and quantum effects using an adiabatic approximation and dual formulation.

Contribution

It introduces a dual formulation to explain vortex statistical interactions and analyzes vortex dynamics, interactions, and quantum effects in a parity-invariant Chern-Simons model.

Findings

Vortices of different types behave like charged particles in a magnetic field.

Vortices of different types can form bound states due to magnetic trapping.

Same-type vortices exhibit no statistical interaction.

Abstract

We apply the adiabatic approximation to investigate the low energy dynamics of vortices in the parity invariant double self-dual Higgs model with only mutual Chern-Simons interaction. When distances between solitons are large they are particles subject to the mutual interaction. The dual formulation of the model is derived to explain the sign of the statistical interaction. When vortices of different types pass one through another they behave like charged particles in magnetic field. They can form a bound state due to the mutual magnetic trapping. Vortices of the same type exhibit no statistical interaction. Their short range interactions are analysed. Possible quantum effects due to the finite width of vortices are discussed.