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

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 $S^3\mathrm{/}{Z}_2$ is also considered, and it is shown that the vacuum associated with broken gauge symmetry is unstable.