Instabilities of Twisted Strings

TL;DR

This paper conducts a linear stability analysis of twisted flux-tube strings in an SU(2) semilocal theory, revealing their exponential instabilities and providing both numerical and semi-analytic insights into their behavior.

Contribution

It offers the first detailed stability analysis of twisted semilocal strings, combining numerical and semi-analytic methods to understand their instabilities and bifurcation structure.

Findings

Twisted strings exhibit exponential growth of instabilities.

A continuous family of unstable eigenmodes exists with harmonic z dependence.

Semi-analytic analysis accurately reproduces numerical results.

Abstract

A linear stability analysis of twisted flux-tubes (strings) in an SU(2) semilocal theory -- an Abelian-Higgs model with two charged scalar fields with a global SU(2) symmetry -- is carried out. Here the twist refers to a relative phase between the two complex scalars (with linear dependence on, say, the $z$ coordinate), and importantly it leads to a global current flowing along the the string. Such twisted strings bifurcate with the Abrikosov-Nielsen-Olesen (ANO) solution embedded in the semilocal theory. Our numerical investigations of the small fluctuation spectrum confirm previous results that twisted strings exhibit instabilities whose amplitudes grow exponentially in time. More precisely twisted strings with a single magnetic flux quantum admit a continuous family of unstable eigenmodes with harmonic $z$ dependence, indexed by a wavenumber $k\in[-k_{\rm m},k_{\rm m}]$. Carrying out a perturbative semi-analytic analysis of the bifurcation, it is found that the purely numerical results are very well reproduced. This way one obtains not only a good qualitative description of the twisted solutions themselves as well as of their instabilities, but also a quantitative description of the numerical results. Our semi-analytic results indicate that in close analogy to the known instability of the embedded ANO vortex a twisted string is also likely to expand in size caused by the spreading out of its magnetic flux.