Static Interactions of non-Abelian Vortices

TL;DR

This paper investigates the interactions of non-Abelian vortices in a U(1) x SU(N) gauge theory, revealing complex behaviors including new regimes analogous to type I/II superconductors and the possibility of bound vortex states.

Contribution

It introduces a detailed analysis of non-Abelian vortex interactions, including numerical and semi-analytical methods, and identifies novel interaction regimes beyond the traditional type I/II classifications.

Findings

Identification of type I*/II* regimes with mixed attractive and repulsive interactions

Discovery of bound states of vortices at non-zero distances

Rich variety of vortex interactions at small separations

Abstract

Interactions between non-BPS non-Abelian vortices are studied in non-Abelian U(1) x SU(N) extensions of the Abelian-Higgs model in four dimensions. The distinctive feature of a non-Abelian vortex is the presence of an internal CP^{N-1} space of orientational degrees of freedom. For fine-tuned values of the couplings, the vortices are BPS and there is no net force between two static parallel vortices at arbitrary distance. On the other hand, for generic values of the couplings the interactions between two vortices depend non-trivially on their relative internal orientations. We discuss the problem both with a numerical approach (valid for small deviations from the BPS limit) and in a semi-analytical way (valid at large vortex separations). The interactions can be classified with respect to their asymptotic property at large vortex separation. In a simpler fine-tuned model, we find two regimes which are quite similar to the usual type I/II Abelian superconductors. In the generic model we find other two new regimes: type I*/II*. Unlike the type I (type II) case, where the interaction is always attractive (repulsive), the type I* and II* have both attractive and repulsive interactions depending on the relative orientation. We have found a rich variety of interactions at small vortex separations. For some values of the couplings, a bound state of two static vortices at a non-zero distance exists.