Self-dual Vortices in the Abelian Chern-Simons Model with Two Complex Scalar Fields

TL;DR

This paper analyzes self-dual vortices in an Abelian Chern-Simons model with two scalar fields, deriving exact equations, angular momentum, and magnetic flux, and studying vortex evolution and interactions.

Contribution

It introduces a detailed analytical framework for vortices with two scalar fields, including topological equations and vortex dynamics, expanding on single-field models.

Findings

Derived exact topological equations for each scalar field.

Calculated magnetic flux linking the two scalar fields.

Found vortex evolution is more complex due to vortex molecule formation.

Abstract

Making use of $\phi$-mapping topological current method, we discuss the self-dual vortices in the Abelian Chern-Simons model with two complex scalar fields. For each scalar field, an exact nontrivial equation with a topological term which is missing in many references is derived analytically. The general angular momentum is obtained. The magnetic flux which relates the two scalar fields is calculated. Furthermore, we investigate the vortex evolution processes, and find that because of the present of the vortex molecule, these evolution processes is more complicated than the vortex evolution processes in the corresponding single scalar field model.