Vilkovisky-DeWitt Effective Action for Einstein Gravity on Kaluza-Klein Spacetimes $M^4\times S^N$

TL;DR

This paper calculates the divergent part of the Vilkovisky-DeWitt effective action for Einstein gravity on specific Kaluza-Klein spacetimes, providing explicit results and analyzing the stability of these configurations.

Contribution

It provides explicit calculations of the divergent effective action and trace anomalies for Einstein gravity on $M^4 imes S^N$ with N=2,4,6, advancing understanding of quantum effects in higher-dimensional spacetimes.

Findings

Explicit divergent effective action results for N=2,4,6

Trace anomalies for gravitons in these spacetimes

Unsuccessful search for stable Kaluza-Klein configurations

Abstract

We evaluate the divergent part of the Vilkovisky-DeWitt effective action for Einstein gravity on even-dimensional Kaluza-Klein spacetimes of the form $M^{4}\times S^{N}$. Explicit results are given for $N$=2, 4, and 6. Trace anomalies for gravitons are also given for these cases. Stable Kaluza-Klein configurations are sought, unsuccessfully, assuming the divergent part of the effective action dominates the dynamics.