Scattering of Vortices at near-critical coupling

TL;DR

This paper extends the geodesic approximation for vortex scattering at critical coupling to near-critical couplings by introducing a perturbed metric and potential, and compares results with numerical simulations.

Contribution

It provides a novel perturbative scheme to analyze vortex scattering near critical coupling, incorporating metric and potential perturbations in the moduli space.

Findings

Good agreement with numerical simulations where radiation effects are minimal.

The method can potentially identify stable bound orbits of vortices.

Extends the geodesic approximation to near-critical coupling scenarios.

Abstract

The scattering of vortices at a critical value of the coupling constant in the Lagrangian can be approximated by a geodesic motion in the moduli space of classical static configurations of vortices. In this paper we give a scheme for generalising this idea to couplings that are near to the critical value. By perturbing a critically coupled field, we show that scattering of vortices at near-critical coupling can be approximated by motion in the original moduli space with a perturbed metric, and a potential. We apply this method to the scattering of two vortices, and compare our results to recent numerical simulations, and find good agreement where the scattering is not highly sensitive to radiation into other field modes. We also investigate the possibility of bound stable orbits of two vortices in the quantum field theory.