Effect of Self-Interaction on Vacuum Energy for Yang-Mills System in Kaluza-Klein Theory

TL;DR

This paper calculates the vacuum energy of a Yang-Mills system in a higher-dimensional space, considering self-interaction effects, and explores how these influence compactification scales and gauge symmetry stability.

Contribution

It provides a detailed analysis of vacuum energy in Kaluza-Klein models with self-interacting Yang-Mills fields, including effects on compactification and gauge symmetry stability.

Findings

Large YM coupling increases the compactification scale.

Vacuum with broken gauge symmetry is unstable.

Self-interaction significantly affects vacuum energy calculations.

Abstract

We calculate the vacuum energy for Yang--Mills (YM) system in the background space-time $M^4 \times S^3$, taking the effect of self-interaction of the YM fields into account. The compactification scale obtained by Candelas--Weinberg mechanism becomes large if the YM coupling is large. The case with an extra space $S^3/Z_2$ is also considered, and it is shown that the vacuum associated with broken gauge symmetry is unstable.