Stability Analysis of The Twisted Superconducting Semilocal Strings

TL;DR

This paper investigates the stability of twisted vortex solutions in a semilocal Abelian Higgs model, finding they lack certain instabilities and may be stable or metastable, with potential implications for vortex dynamics.

Contribution

It provides a detailed stability analysis of twisted vortices, revealing their stability against homogeneous and short-wavelength inhomogeneous perturbations, and identifies a specific long-wavelength instability.

Findings

Twisted vortices are stable against homogeneous and short-wavelength perturbations.

Long-wavelength perturbations induce a 'sausage' instability similar to fluid and gravitational instabilities.

Short vortex segments may be perturbatively stable, possibly forming stable vortex loops.

Abstract

We study the stability properties of the twisted vortex solutions in the semilocal Abelian Higgs model with a global $\mathbf{SU}(2)$ invariance. This model can be viewed as the Weinberg-Salam theory in the limit where the non-Abelian gauge field decouples, or as a two component Ginzburg-Landau theory. The twisted vortices are characterized by a constant global current ${\cal I}$, and for ${\cal I}\to 0$ they reduce to the semilocal strings, that is to the Abrikosov-Nielsen-Olesen vortices embedded into the semilocal model. Solutions with ${\cal I}\neq 0$ are more complex and, in particular, they are {\it less energetic} than the semilocal strings, which makes one hope that they could have better stability properties. We consider the generic field fluctuations around the twisted vortex within the linear perturbation theory and apply the Jacobi criterion to test the existence of the negative modes in the spectrum of the fluctuation operator. We find that twisted vortices do not have the homogeneous instability known for the semilocal strings, neither do they have inhomogeneous instabilities whose wavelength is less than a certain critical value. This implies that short enough vortex pieces are perturbatively stable and suggests that small vortex loops could perhaps be stable as well. For longer wavelength perturbations there is exactly one negative mode in the spectrum whose growth entails a segmentation of the uniform vortex into a non-uniform, `sausage like' structure. This instability is qualitatively similar to the hydrodynamical Plateau-Rayleigh instability of a water jet or to the Gregory-Laflamme instability of black strings in the theory of gravity in higher dimensions.