Dynamics of Non-Abelian Vortices

TL;DR

This paper investigates the complex dynamics of non-Abelian vortices in (2+1)-dimensional U(N) gauge theories, revealing unique scattering behaviors, energy transfer mechanisms, and bound states due to internal orientational moduli.

Contribution

It introduces a detailed analysis of non-Abelian vortex scattering using moduli space metrics, highlighting new dynamical features absent in Abelian vortices.

Findings

Energy transfer between real space and internal moduli

Scattering angle depends on vortex orientations

Existence of bound vortex states in mass-deformed theories

Abstract

The scattering is studied using moduli space metric for well-separated vortices of non-Abelian vortices in (2+1)-dimensional U(N) gauge theories with N Higgs fields in the fundamental representation. Unlike vortices in the Abelian-Higgs model, dynamics of non-Abelian vortices has a lot of new features; The kinetic energy in real space can be transfered to that of internal orientational moduli and vice versa, the energy and charge transfer between two vortices, the scattering angle of collisions with a fixed impact parameter depends on the internal orientations, and some resonances appear due to synchronization of the orientations. Scattering of dyonic non-Abelian vortices in a mass deformed theory is also studied. We find a bound state of two vortices moving along coils around a circle, like a loop of a phone code.