Dynamics of critical vortices on the torus and on the plane

TL;DR

This paper constructs the metric tensor for vortex solutions in the Abelian Higgs model on a torus, analyzing vortex dynamics and scattering, with results applicable to large-volume limits approaching the plane.

Contribution

It introduces a novel application of the Bradlow parameter expansion to derive the metric tensor for vortex solutions on a torus, enabling detailed study of vortex dynamics.

Findings

Metric tensor constructed using Bradlow expansion

Vortex dynamics approximated by geodesic motion

Results interpolate between small torus and plane limits

Abstract

We use the Bradlow parameter expansion to construct the metric tensor in the space of solutions of the Bogomolny equations for the Abelian Higgs model on a two-dimensional torus. Using this metric we study the dynamics and scattering of vortices on the torus within the geodesic approximation. For small torus volumes the metric is determined in terms of a small number of parameters. For large volumes the results provide a very precise approximation to the metric and dynamics on the plane.