Moduli Space Dynamics of a First-Order Vortex System

TL;DR

This paper investigates the moduli space dynamics of vortices in the Jackiw-Pi model, deriving exact metrics, effective Lagrangians, and exploring duality between particles and vortices.

Contribution

It introduces a method to derive the moduli space metric for first-order vortex systems by converting the Lagrangian into a second order form, and explores vortex responses and dualities.

Findings

Exact metrics for simple vortex cases obtained.

Vortices' response to external U(1) fields described.

Duality between particles and vortices clarified.

Abstract

The moduli space dynamics of vortices in the Jackiw-Pi model where a non-relativistic Schrodinger field couples minimally to Chern-Simons gauge field, is considered. It is shown that the difficulties in direct application of Manton's method to obtain a moduli-space metric in the first order system can be circumvented by turning the Lagrangian into a second order system. We obtain exact metrics for some simple cases and describe how the vortices respond to an external U(1) field. We then construct an effective Lagrangian describing dynamics of the vortices. In addition, we clarify strong-weak coupling duality between fundamental particles and vortices.