Non-Abelian vortices with a twist

Abstract

Non-Abelian flux-tube (string) solutions carrying global currents are found in the bosonic sector of four-dimensional $\mathcal{N}=2$ supersymmetric gauge theories. The specific model considered here possesses ${U(2)}_{\text{local}}\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(2)}_{\text{global}}$ symmetry, with two scalar doublets in the fundamental representation of SU(2). We construct string solutions that are stationary and translationally symmetric along the ${x}^{3}$ direction, and they are characterized by a matrix phase between the two doublets, referred to as ``twist.'' Consequently, twisted strings have nonzero (global) charge, momentum, and in some cases even angular momentum per unit length. The planar cross section of a twisted string corresponds to a rotationally symmetric, charged non-Abelian vortex, satisfying first-order Bogomolny-type equations and second-order Gauss constraints. Interestingly, depending on the nature of the matrix phase, some of these solutions even break cylindrical symmetry in ${\mathbb{R}}^{3}$. Although twisted vortices have higher energy than the untwisted ones, they are expected to be linearly stable since one can keep their charge (or twist) fixed with respect to small perturbations.