Interaction energy of Chern-Simons vortices in the gauged O(3) sigma model

TL;DR

This paper computes the interaction energy of gauged O(3) Chern-Simons vortices at infinite separation, revealing how the energy depends on the coupling constant and identifying conditions for vortex attraction or repulsion.

Contribution

It provides a detailed calculation of vortex interaction energy in the gauged O(3) sigma model with Chern-Simons terms, highlighting the role of the coupling constant in vortex dynamics.

Findings

Vortices attract when λ > 1

Vortices repel when λ < 1

Energy bound is saturated at λ = 1

Abstract

The purpose of this Letter is to present a computation of the interaction energy of gauged O(3) Chern-Simons vortices which are infinitely separated. The results will show the behaviour of the interaction energy as a function of the constant coupling the potential, which measures the relative strength of the matter self-coupling and the electromagnetic coupling. We find that vortices attract each other for $\lambda > 1 $ and repel when $\lambda < 1 $. When $\lambda =1 $ there is a topological lower bound on the energy. It is possible to saturate the bound if the fields satisfy a set of first order partial differential equations.