Vortex dynamics in nonrelativistic Abelian Higgs model

TL;DR

This paper investigates vortex dynamics in a nonrelativistic Abelian Higgs model, deriving equations for vortex contour properties and analyzing how interactions with fermion backgrounds affect helicity conservation.

Contribution

It generalizes hydrodynamic vortex equations to gauge vortices, including effects of fermion backgrounds, and studies helicity conservation in this context.

Findings

Helicity conservation is broken by phase and modulus excitations.

Gauge field coupling with fermion background affects vortex dynamics.

Derived equations extend Betchov-Da Rios equations to gauge vortices.

Abstract

The dynamics of the gauge vortex with arbitrary form of a contour is considered in the framework of the nonrelativistic Abelian Higgs model, including the possibility of the gauge field interaction with the fermion asymmetric background. The equations for the time derivatives of the curvature and the torsion of the vortex contour generalizing the Betchov-Da Rios equations in hydrodynamics, are obtained. They are applied to study the conservation of helicity of the gauge field forming the vortex, twist, and writhe numbers of the vortex contour. It is shown that the conservation of helicity is broken when both terms in the equation of the vortex motion are present, first due to the exchange of excitations of the phase and modulus of the scalar field and the second one due to the coupling of the gauge field forming the vortex, with the fermion asymmetric background.