Stability Analysis of The Twisted Superconducting Semilocal Strings

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 $\mathcal{I}$, and for $\mathcal{I}\to 0$ they reduce to the semilocal strings, that is to the Abrikosov-Nielsen-Olesen vortices embedded into the semilocal model. Solutions with $\mathcal{I}\ne 0$ 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.

33 pages, 6 figures. to appear in Nuclear Physics B

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Cited by in corpus (16)

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• Stable Cosmic Vortons
• Winding Hopfions on R^2 x S^1
• Superconducting non-Abelian vortices in Weinberg-Salam theory -- electroweak thunderbolts
• Stability analysis of black holes by the $S$-deformation method for coupled systems
• Gravitating superconducting solitons in the (3+1)-dimensional Einstein gauged non-linear sigma-model
• Vortices and magnetic bags in Abelian models with extended scalar sectors and some of their applications
• Stabilisation of semilocal strings by dark scalar condensates
• Vortices with scalar condensates in two-component Ginzburg-Landau systems
• Can type II Semi-local cosmic strings form?
• Instabilities of Twisted Strings
• Vortex matter in $U(1)\times U(1)\times {\mathbb{Z}}_2$ phase-separated superconducting condensates
• Superconducting and Spinning Non-Abelian Flux Tubes
• Stability Analysis of Superconducting Electroweak Vortices
• Electroweak strings with dark scalar condensates and their (in)stability
• Non-Abelian Vortices with a Twist