Type I Non-Abelian Superconductors in Supersymmetric Gauge Theories

TL;DR

This paper investigates non-Abelian vortices in a supersymmetric gauge theory, revealing their attractive or repulsive interactions, effective descriptions, and stability properties, thus extending the understanding of non-Abelian superconductors.

Contribution

It introduces a non-Abelian generalization of type I superconductors within supersymmetric gauge theories, analyzing vortex interactions, effective models, and stability of different vortex solutions.

Findings

Vortices exhibit both attractive and repulsive forces depending on orientation.

Effective potential depends on vortex separation and internal orientation.

Two distinct solutions for coincident vortices with different tensions and stability.

Abstract

Non-BPS non-Abelian vortices with CP^1 internal moduli space are studied in an N=2 supersymmetric U(1) x SU(2) gauge theory with softly breaking adjoint mass terms. For generic internal orientations the classical force between two vortices can be attractive or repulsive. On the other hand, the mass of the scalars in the theory is always less than that of the vector bosons; also, the force between two vortices with the same CP^1 orientation is always attractive: for these reasons we interpret our model as a non-Abelian generalization of type I superconductors. We compute the effective potential in the limit of two well separated vortices. It is a function of the distance and of the relative colour-flavour orientation of the two vortices; in this limit we find an effective description in terms of two interacting CP^1 sigma models. In the limit of two coincident vortices we find two different solutions with the same topological winding and, for generic values of the parameters, different tensions. One of the two solutions is described by a CP^1 effective sigma model, while the other is just an Abelian vortex without internal degrees of freedom. For generic values of the parameters, one of the two solutions is metastable, while there are evidences that the other one is truly stable.