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

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.