  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.
