Fermion Energies in the Background of a Cosmic String

TL;DR

This paper investigates the quantum stabilization of cosmic strings through fermion coupling, demonstrating that realistic fermion masses can stabilize strings without requiring extreme parameters.

Contribution

It provides a detailed analysis of quantum stabilization mechanisms for cosmic strings via fermion interactions within a simplified standard model framework.

Findings

Fermion charge stabilizes cosmic strings under certain mass conditions.

Neutral strings are energetically unfavorable, ensuring overall stability.

Realistic fermion masses suffice for string stabilization without extreme couplings.

Abstract

We provide a thorough exposition, including technical and numerical details, of previously published results on the quantum stabilization of cosmic strings. Stabilization occurs through the coupling to a heavy fermion doublet in a reduced version of the standard model. We combine the vacuum polarization energy of fermion zero-point fluctuations and the binding energy of occupied energy levels, which are of the same order in a semi-classical expansion. Populating these bound states assigns a charge to the string. We show that strings carrying fermion charge become stable if the electro-weak bosons are coupled to a fermion that is less than twice as heavy as the top quark. The vacuum remains stable in our model, because neutral strings are not energetically favored. These findings suggests that extraordinarily large fermion masses or unrealistic couplings are not required to bind a cosmic string in the standard model.