First and Second Order Vortex Dynamics

TL;DR

This paper investigates vortex dynamics in Abelian Higgs theory, revealing how adding a Chern-Simons term introduces a first order velocity term, and explores related angular momentum and potential effects.

Contribution

It demonstrates the emergence of a linear velocity term in vortex dynamics when a Chern-Simons term is included, extending the understanding of vortex motion beyond second order.

Findings

Addition of Chern-Simons term introduces a first order velocity term.

Angular momentum analysis supports the modified vortex dynamics.

Exploration of background charge effects and harmonic potentials on vortices.

Abstract

The low energy dynamics of vortices in selfdual Abelian Higgs theory is of second order in vortex velocity and characterized by the moduli space metric. When Chern-Simons term with small coefficient is added to the theory, we show that a term linear in vortex velocity appears and can be consistently added to the second order expression. We provides an additional check of the first and second order terms by studying the angular momentum in the field theory. We briefly explore other first order term due to small background electric charge density and also the harmonic potential well for vortices given by the moment of inertia.