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 SU(2) invariance. This model can be viewed as the WeinbergSalam 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 I, and for I → 0 they reduce to the semilocal strings, that is to the AbrikosovNielsen-Olesen vortices embedded into the semilocal model. Solutions with I = 0 are more complex and, in particular, they are 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.

Vortices and magnetic bags in Abelian models with extended scalar sectors and some of their applications

“…[40,41,47,48,49]. It has been shown that in the semi-local model for β > 1, the instability of the embedded ANO vortex corresponds to its bifurcation with a oneparameter family of solutions, which are, however, still unstable [50,51,52,53]. The existence of a lowest energy limit of this family of solutions with a less symmetric potential has been demonstrated in Ref.…”

“…The SU(2) symmetric case, has been considered in Ref. [50,51,52]. Here, the Lagrangian of the theory, Eq.…”

“…For twisted vortices, 0 < ω ≤ ω b , the results are similar to those in the case of an SU(2) symmetric potential (see Refs. [50,51,52]): fistly, the mode corresponding to the lovest value of the squared frequency Ω 2 is a one-parameter deformation of the instability mode of the embedded ANO vortex. Second, for all values 0 < ω ≤ ω b which were available to our numerical code, we have found one unstable mode in the ℓ = 0 sector, i.e., the instability of the embedded ANO vortex persisted for all examined twisted vortices, and, for lower values of the twist, ω, the value of |Ω 2 | got also smaller.…”

Vortices with scalar condensates in two-component Ginzburg–Landau systems

“…The SU(2) symmetric model, called semilocal has been considered in Refs. [29,30,31,32,33,34,42,43,44].…”

Non-Abelian vortices with a twist

“…In the case of the twisted semilocal vortices of Ref. [17], with ω α timelike, such deformations indeed exist [21], however, they correspond to the same type of instability as those of ANO vortices embedded in a two-component extended Abelian Higgs model [22]. In the present case, however, such potential instabilities are absent.…”