Kibble mechanism for electroweak magnetic monopoles and magnetic fields

TL;DR

This paper extends the Kibble mechanism to electroweak theory, proposing new criteria for monopole and string detection, and explores how magnetic fields generated by monopoles evolve cosmologically.

Contribution

It introduces a novel perspective on the vacuum manifold in electroweak theory and develops criteria for detecting monopoles and Z-strings during symmetry breaking.

Findings

Magnetic field spectrum follows B_λ ∝ λ^{-2}

Electroweak monopoles can generate cosmologically relevant magnetic fields

Magnetic fields persist despite monopole annihilation due to Z-strings

Abstract

The vacuum manifold of the standard electroweak model is a three-sphere when one considers homogeneous Higgs field configurations. For inhomogeneous configurations we argue that the vacuum manifold is the Hopf fibered three sphere and that this viewpoint leads to general criteria to detect electroweak monopoles and Z-strings. We extend the Kibble mechanism to study the formation of electroweak monopoles and strings during electroweak symmetry breaking. The distribution of magnetic monopoles produces magnetic fields that have a spectrum $B_\lambda \propto \lambda^{-2}$, where $\lambda$ is a smearing length scale. Even as the magnetic monopoles annihilate due to the confining Z-strings, the magnetic field evolves with the turbulent plasma and may be relevant for cosmological observations.