Inducing the Lovelock action

TL;DR

This paper clarifies how the Gauss-Bonnet term affects divergences in Einstein-Gauss-Bonnet gravity, showing it does not introduce new divergences in four dimensions but does in higher dimensions, challenging previous conjectures.

Contribution

It demonstrates that the Gauss-Bonnet term modifies the graviton operator without adding divergences in four dimensions, and clarifies its role in higher-dimensional divergences.

Findings

No new on-shell divergences at one loop in d=4

Gauss-Bonnet term generates divergences in six dimensions

The conjecture about eight-dimensional Euler term is false

Abstract

We re-analyze a possible ambiguity in the application of dimensional regularization to Einstein-Gauss-Bonnet gravity, arising from the way one treats the Gauss-Bonnet term. It is demonstrated that the addition of such a term to the action gives rise to a non-minimal graviton wave operator, but does not produce new on shell divergences at one loop order in d=4. However, from a d-dimensional perspective the Gauss-Bonnet term is shown to generate new divergences in the form of the six-dimensional Euler density. The conjecture that one would next produce the eight-dimensional Euler term is shown to be false.