Stability Analysis of The Twisted Superconducting Semilocal Strings - High Energy Physics - TheoryReport as inadecuate

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Abstract: We study the stability properties of the twisted vortex solutions in thesemilocal Abelian Higgs model with a global $\mathbf{SU}2$ invariance. Thismodel can be viewed as the Weinberg-Salam theory in the limit where thenon-Abelian gauge field decouples, or as a two component Ginzburg-Landautheory. The twisted vortices are characterized by a constant global current${\cal I}$, and for ${\cal I}\to 0$ they reduce to the semilocal strings, thatis to the Abrikosov-Nielsen-Olesen vortices embedded into the semilocal model.Solutions with ${\cal I} eq 0$ are more complex and, in particular, they are{\it less energetic} than the semilocal strings, which makes one hope that theycould have better stability properties. We consider the generic fieldfluctuations around the twisted vortex within the linear perturbation theoryand apply the Jacobi criterion to test the existence of the negative modes inthe spectrum of the fluctuation operator. We find that twisted vortices do nothave the homogeneous instability known for the semilocal strings, neither dothey have inhomogeneous instabilities whose wavelength is less than a certaincritical value. This implies that short enough vortex pieces are perturbativelystable and suggests that small vortex loops could perhaps be stable as well.For longer wavelength perturbations there is exactly one negative mode in thespectrum whose growth entails a segmentation of the uniform vortex into anon-uniform, `sausage like- structure. This instability is qualitativelysimilar to the hydrodynamical Plateau-Rayleigh instability of a water jet or tothe Gregory-Laflamme instability of black strings in the theory of gravity inhigher dimensions.

Author: Julien Garaud, Mikhail S. Volkov


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