1-Loop Divergences of Quantum Gravity Using Conformal Parametrization

TL;DR

This paper computes one-loop divergences in quantum gravity using a conformal parametrization, revealing gauge independence and connections to earlier results, with implications for conformal gravity theories.

Contribution

It introduces a new conformal parametrization approach for quantum gravity and verifies gauge independence of divergences, aligning with classical results by t'Hooft and Veltman.

Findings

Divergences are independent of conformal gauge parameter on-shell.

A special gauge reproduces classical divergence results.

Conformal invariance helps restore divergences in conformal gravity.

Abstract

We calculate the one-loop divergences for quantum gravity with cosmological constant, using new parametrization of quantum metric. The conformal factor of the metric is treated as an independent variable. As a result the theory possesses an additional degeneracy and one needs an extra conformal gauge fixing. We verify the on shell independence of the divergences from the parameter of the conformal gauge fixing, and find a special conformal gauge in which the divergences coincide with the ones obtained by t'Hooft and Veltman (1974). Using conformal invariance of the counterterms one can restore the divergences for the conformal metric-scalar gravity.