Gauges and functional measures in quantum gravity II: Higher derivative gravity

TL;DR

This paper calculates one-loop divergences in a higher-derivative quantum gravity theory, exploring gauge and parametrization dependencies, and revealing invariance under a duality transformation involving densitized metrics.

Contribution

It provides the first detailed computation of divergences in higher-derivative gravity including Ricci squared terms on Einstein backgrounds, analyzing gauge and parametrization effects.

Findings

Certain gauge and parametrization choices reduce parameter dependence.

Results are invariant under a duality transformation of the densitized metric.

The study advances understanding of quantum corrections in higher-derivative gravity.

Abstract

We compute the one-loop divergences in a higher-derivative theory of gravity including Ricci tensor squared and Ricci scalar squared terms, in addition to the Hilbert and cosmological terms, on an (generally off-shell) Einstein background. We work with a two-parameter family of parametrizations of the graviton field, and a two-parameter family of gauges. We find that there are some choices of gauge or parametrization that reduce the dependence on the remaining parameters. The results are invariant under a recently discovered "duality" that involves the replacement of the densitized metric by a densitized inverse metric as the fundamental quantum variable.