From BPS geodesics to mode-driven dynamics in the scattering of multiple BPS vortices

TL;DR

This paper investigates how excitation of a massive bound mode alters the geodesic motion of BPS vortices in the Abelian-Higgs model, revealing mode-driven forces that can significantly change vortex trajectories and increase chaos.

Contribution

It introduces the concept of mode-driven forces affecting vortex dynamics, extending the understanding of BPS vortex scattering beyond pure geodesic motion.

Findings

Geodesics with enhanced symmetry remain unchanged despite mode excitation.

Mode-driven forces can significantly alter vortex trajectories in generic collisions.

Enhanced chaos observed in vortex formation due to mode effects.

Abstract

We analyze how the geodesic motion in the 3- and 4-vortex sectors of the Abelian-Higgs model at critical coupling is deformed by the excitation of a massive bound mode. We find that the geodesics corresponding to BPS solutions with enhanced symmetry remain unchanged, although the direction of the actual motion depends on the mode-generated force, i.e., a force arising from the change of the mode frequency along the geodesic. In a generic case, for example in head-on collisions between the axially symmetric 1- and 2-vortex or between two 2-vortices, the vortex trajectories can differ strongly from the BPS geodesic. This enhances the chaotic behavior in the formation of the final state.