Conformal Tensors via Lovelock Gravity

TL;DR

This paper develops higher-curvature, conformally invariant tensors within Lovelock gravity and introduces new gravity theories in dimensions multiple of four based on these tensors.

Contribution

It constructs higher-curvature conformal tensors in Lovelock gravity and proposes new conformally invariant gravity theories in dimensions 4k.

Findings

Defined higher-curvature Weyl, Schouten, Cotton, Bach tensors in Lovelock gravity.

Introduced new conformally invariant gravity models in D=4k dimensions.

Extended properties of classical conformal tensors to higher curvature Lovelock context.

Abstract

Constructs from conformal geometry are important in low dimensional gravity models, while in higher dimensions the higher curvature interactions of Lovelock gravity are similarly prominent. Considering conformal invariance in the context of Lovelock gravity leads to natural, higher-curvature generalizations of the Weyl, Schouten, Cotton and Bach tensors, with properties that straightforwardly extend those of their familiar counterparts. As a first application, we introduce a new set of conformally invariant gravity theories in D=4k dimensions, based on the squares of the higher curvature Weyl tensors.