The effective action and equations of motion of curved local and global vortices: Role of the field excitations

TL;DR

This paper derives effective actions and equations of motion for curved local and global vortices, highlighting the role of field excitations like the Bogolyubov-Anderson mode in their dynamics.

Contribution

It provides a unified derivation of vortex effective actions incorporating field excitations, and computes their impact on vortex forces and masses.

Findings

Field excitations cancel long-distance divergences in local vortices.

Effective actions for global vortices match Greiter-Wilczek-Witten form.

Derived equations of motion including excitation effects, solved for various displacements.

Abstract

The effective actions for both local and global curved vortices are derived, based on the derivative expansion of the corresponding field theoretic actions of the nonrelativistic Abelian Higgs and Goldstone models. The role of excitations of the modulus and the phase of the scalar field and of the gauge field (the Bogolyubov-Anderson mode) emitted and reabsorbed by vortices is elucidated. In case of the local (gauge) magnetic vortex, they are necessary for cancellation of the long distance divergence when using the transverse form of the electric gauge field strength of the background field. In case of global vortex taking them into account results in the Greiter-Wilczek-Witten form of the effective action for the Goldstone mode. The expressions for transverse Magnus-like force and the vortex effective mass for both local and global vortices are found. The equations of motion of both type of vortices including the terms due to the field excitations are obtained and solved in cases of large and small contour displacements.