On Instability of Squashed Spheres in the Kaluza-Klein Theory

TL;DR

This paper investigates the stability of extra dimensions in Kaluza-Klein theories against homogeneous deformations, considering quantum fluctuations of matter fields at one-loop level, with specific focus on models involving $S^3$ and $S^7$ spheres.

Contribution

It provides a detailed analysis of the stability conditions of squashed spheres in Kaluza-Klein models, incorporating quantum effects of matter fields, which was not thoroughly examined before.

Findings

Stability depends on scalar matter field coupling to scalar curvature.

Quantum fluctuations influence the effective potential and stability.

Results vary between different sphere models, such as $S^3$ and $S^7$.

Abstract

We study in Kaluza-Klein theories stability of the extra space against "squashing", in other words, the homogeneous deformation. Quantum fluctuations of matter fields at one-loop level are taken into consideration. We calculate the effective potential in models of the type, $M^4\times S^3$ and $M^4\times S^7$. It is found that in the case of scalar matter fields the stability depends on the coupling to the scalar curvature.