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

TL;DR

This paper analyzes classical electroweak vortex solutions carrying large electric currents, revealing their structure, stability, and potential to form stable loops called electroweak vortons, which could transfer charge and resemble thunderbolts.

Contribution

It provides a detailed analysis of current-carrying electroweak vortices, including their structure, stability, and the possibility of forming stable loops, extending understanding of non-Abelian vortex solutions.

Findings

Vortices carry extremely large electric currents, up to billions of Amperes.

Large current vortices have a compact core and a large surrounding region where symmetry is restored.

Finite vortex segments may be perturbatively stable and could form stable loops called electroweak vortons.

Abstract

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.