arXiv subjects

Julien Garaud

Publications and source records attributed to Julien Garaud.

39 records · Page 3Linked to original sources

arXiv2010

Stability Analysis of Superconducting Electroweak Vortices

We carry out a detailed stability analysis of the superconducting vortex solutions in the Weinberg-Salam theory described in Nucl.Phys. B826 (2010) 174. These vortices are characterized by constant electric current $I$ and electric charge density $I_0$, for ${I}\to 0$ they reduce to Z strings. We consider the generic field fluctuations around the vortex and apply the functional Jacobi criterion to detect the negative modes in the fluctuation operator spectrum. We find such modes and determine their dispersion relation, they turn out to be of two different types, according to their spatial behavior. There are non-periodic in space negative modes, which can contribute to the instability of infinitely long vortices, but they can be eliminated by imposing the periodic boundary conditions along the vortex. There are also periodic negative modes, but their wavelength is always larger than a certain minimal value, so that they cannot be accommodated by the short vortex segments. However, even for the latter there remains one negative mode responsible for the homogeneous expansion instability. This mode may probably be eliminated when the vortex segment is bent into a loop. This suggests that small vortex loops balanced against contraction by the centrifugal force could perhaps be stable.

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arXiv2009

Superconducting non-Abelian vortices in Weinberg-Salam theory -- electroweak thunderbolts

We present a detailed analysis of classical solutions in the bosonic sector of the electroweak theory which describe vortices carrying a constant electric current ${\cal I}$. These vortices exist for any value of the Higgs boson mass and for any weak mixing angle, and in the zero current limit they reduce to Z strings. Their current is produced by the condensate of vector W bosons and typically it can attain billions of Amperes. For large ${\cal I}$ the vortices show a compact condensate core of size $\sim 1/{\cal I}$, embedded into a region of size $\sim{\cal I}$ where the electroweak gauge symmetry is completely restored, followed by a transition zone where the Higgs field interpolates between the symmetric and broken phases. Outside this zone the fields are the same as for the ordinary electric wire. An asymptotic approximation of the large ${\cal I}$ solutions suggests that the current can be {arbitrarily} large, due to the scale invariance of the vector boson condensate. Finite vortex segments whose length grows with ${\cal I}$ seem to be perturbatively stable. This suggests that they can transfer electric charge between different regions of space, similarly to thunderbolts. It is also possible that they can form loops stabilized by the centrifugal force -- electroweak vortons.

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arXiv2008

Stability Analysis of The Twisted Superconducting Semilocal Strings

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.

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