Quantum stabilization of a hedgehog type of cosmic string

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.Comment: 34 page

Attractive Electromagnetic Casimir Stress on a Spherical Dielectric Shell

Based on calculations involving an idealized boundary condition, it has long been assumed that the stress on a spherical conducting shell is repulsive. We use the more realistic case of a Drude dielectric to show that the stress is attractive, matching the generic behavior of Casimir forces in electromagnetism. We trace the discrepancy between these two cases to interactions between the electromagnetic quantum fluctuations and the dielectric material.Comment: Five pages, one figure, pdflatex, matches version to be pusblished in Phys Lett

Stable charged cosmic strings

We study the quantum stabilization of a cosmic string by a heavy fermion doublet in a reduced version of the standard model. We show that charged strings, obtained by populating fermionic bound state levels, become stable if the electro--weak bosons are coupled to a fermion that is less than twice as heavy as the top quark. This result suggests that extraordinarily large fermion masses or unrealistic couplings are not required to bind a cosmic string in the standard model. Numerically we find the most favorable string profile to be a simple "trough" in the Higgs vev of radius $\approx 10^{-18}\,\mathrm{m}$. The vacuum remains stable in our model, because neutral strings are not energetically favored.Comment: 5 pages, 3 figures, version to be published in Phys. Rev. Let

Spectral Methods for Coupled Channels with a Mass Gap

We develop a method to compute the vacuum polarization energy for coupled scalar fields with different masses scattering off a background potential in one space dimension. As an example we consider the vacuum polarization energy of a kink-like soliton built from two real scalar fields with different mass parameters.Comment: 14 pages, 5 figures, matches journal version, references added (surprisingly many

Quantum stabilization of Z-strings, a status report on D=3+1 dimensions

We investigate an extension to the phase shift formalism for calculating one-loop determinants. This extension is motivated by requirements of the computation of Z-string quantum energies in D=3+1 dimensions. A subtlety that seems to imply that the vacuum polarization diagram in this formalism is (erroneously) finite is thoroughly investigated.Comment: Based on talk by O.S. at QFEXT07, Leipzig Sept. 2007. 8 page