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

TL;DR

This paper extends the phase shift formalism to accurately compute quantum energies of Z-strings in 3+1 dimensions, addressing a subtlety related to vacuum polarization diagrams and their finiteness.

Contribution

It introduces an extension to the phase shift formalism specifically for Z-string quantum energy calculations in four-dimensional spacetime.

Findings

Identifies a subtlety in the vacuum polarization diagram's finiteness.

Provides a refined method for one-loop determinant calculations.

Clarifies the implications for quantum stability of Z-strings.

Abstract

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.