Gauge Invariance and Vacuum Energies of Non-Abelian String-Configurations

TL;DR

This paper presents an improved numerical method for calculating the fermion contribution to the vacuum polarization energy of non-Abelian string configurations, confirming gauge invariance and demonstrating that the vacuum energy is negligible compared to fermion mass.

Contribution

The paper introduces a new numerical approach that verifies gauge invariance and supports spectral methods for vacuum energy calculations in non-Abelian gauge theories.

Findings

Vacuum energy in MS-bar scheme is very small compared to fermion mass.

Numerical results for on-shell scheme are consistent with theoretical expectations.

Method confirms gauge invariance of vacuum polarization energies.

Abstract

We improve on a method to compute the fermion contribution to the vacuum polarization energy of string-like configurations in a non-Abelian gauge theory. We establish the new method by numerically verifying the invariance under (a subset of) local gauge transformations. This also provides further support for the use of spectral methods to compute vacuum polarization energies in general. We confirm that the vacuum energy in the MS-bar renormalization scheme is tiny as compared to the mass of the fluctuating fermion field. Numerical results for the physical on-shell scheme are also presented.