Wilson-Loop Symmetry Breaking Reexamined

TL;DR

This paper reexamines gauge field vacuum energy splitting on a non-simply connected space, confirming previous results through one-loop calculations and addressing questions raised by prior researchers.

Contribution

It provides a detailed one-loop calculation of gauge vacuum energy splitting on $S^3/Z_2$, confirming earlier findings and clarifying previous uncertainties.

Findings

Confirmed energy splitting results at one-loop level

Provided a solution to previously posed questions

Validated the calculation method for gauge vacua on non-simply connected spaces

Abstract

The splitting in energy of gauge field vacua on the non-simply connected space $S^3/Z_2$ is reconsidered. We show the calculation to the one-loop level for a Yang-Mills vector with a ghost field. We confirm our previous result and give a solution to the question posed by Freire, Rom\~ao and Barroso.