The Gauss-Bonnet Coupling Constant in Classically Scale-Invariant Gravity

TL;DR

This paper analyzes the renormalization of higher-derivative gravity with a focus on the Gauss-Bonnet coupling, demonstrating its dependence on other couplings and consistency in four dimensions, with implications for nonperturbative effects.

Contribution

It introduces a technique to determine the Gauss-Bonnet coupling dependence on other couplings and shows its consistency in four-dimensional gravity at all perturbation orders.

Findings

Gauss-Bonnet coupling depends on primary couplings

Consistency with four-dimensional Gauss-Bonnet relation

Potential nonperturbative effects from instantons

Abstract

We discuss the renormalization of higher-derivative gravity, both without and with matter fields, in terms of two primary coupling constants rather than three. A technique for determining the dependence of the Gauss-Bonnet coupling constant on the remaining couplings is explained, and consistency with the local form of the Gauss-Bonnet relation in four dimensions is demonstrated to all orders in perturbation theory. A similar argument is outlined for the Hirzebruch signature and its coupling. We speculate upon the potential implications of instantons on the associated nonperturbative coupling constants.