# Quantum stabilization of a hedgehog type of cosmic string

## TL;DR

This paper explores how quantum fermion fluctuations can stabilize hedgehog-type cosmic strings within a simplified electroweak model, revealing configurations that are energetically favored and potentially stable.

## Contribution

It introduces a novel analysis of hedgehog cosmic strings with fermion quantum corrections, extending previous models to include pseudoscalar fields and developing spectral methods for stability assessment.

## Key findings

- Hedgehog strings can be stabilized by fermion quantum effects.
- Certain parameter regimes favor stable, bound fermion states on the strings.
- Deformed Higgs fields enhance binding without large gradients.

## Abstract

Within a slightly simplified version of the electroweak standard model we investigate the stabilization of cosmic strings by fermion quantum fluctuations. Previous studies of quantum energies considered variants of the Nielsen-Olesen profile embedded in the electroweak gauge group and showed that configurations are favored for which the Higgs vacuum expectation value drops near the string core and the gauge field is suppressed. This work found that the strongest binding was obtained from strings that differ significantly from Nielsen-Olesen configurations, deforming essentially only the Higgs field in order to generate a strong attraction without inducing large gradients. Extending this analysis, we consider the leading quantum correction to the energy per unit length of a hedgehog type string, which, in contrast to the Nielsen-Olesen configuration, contains a pseudoscalar field. To employ the spectral method we develop the scattering and bound state problems for fermions in the background of a hedgehog string. Explicit occupation of bound state levels leads to strings that carry the quantum numbers of the bound fermions. We discuss the parameter space for which stable, hedgehog type cosmic strings emerge and reflect on phenomenological consequences of these findings.