Vacuum Energies of Non--Abelian String--Configurations in 3+1 Dimensions

TL;DR

This paper introduces a new method to calculate the fermion vacuum polarization energy of non-abelian string configurations in 3+1 dimensions, overcoming previous technical challenges and demonstrating small energy contributions in a specific renormalization scheme.

Contribution

The authors develop a gauge-invariant, scalable approach to compute vacuum energies for non-abelian strings, addressing longstanding computational obstacles.

Findings

Vacuum energy is small in the MS-bar scheme.

Method overcomes previous technical barriers.

Framework applicable to other renormalization schemes.

Abstract

We develop a method to compute the fermion contribution to the vacuum polarization energy of string--like configurations in a non--abelian gauge theory. This calculation has been hampered previously by a number of technical obstacles. We use gauge invariance of the energy and separation of length scales in the energy density to overcome these obstacles. We present a proof-of-principle investigation that shows that this energy is small in the MS-bar renormalization scheme. The generalization to other schemes is straightforward.