A proper-time cure for the conformal sickness in quantum gravity

TL;DR

This paper proposes a non-perturbative method to resolve the conformal divergence in quantum gravity path integrals by using proper-time gauge fixing and a Faddeev-Popov determinant, supported by 3D perturbative analysis.

Contribution

It introduces a proper-time gauge fixing approach that cancels conformal divergences non-perturbatively in quantum gravity path integrals, inspired by Lorentzian triangulations.

Findings

Conformal divergence is canceled non-perturbatively by the Faddeev-Popov determinant.

Proper-time gauge fixing facilitates a well-defined gravitational path integral.

Perturbative calculations support the proposed cancellation mechanism.

Abstract

Starting from the space of Lorentzian metrics, we examine the full gravitational path integral in 3 and 4 space-time dimensions. Inspired by recent results obtained in a regularized, dynamically triangulated formulation of Lorentzian gravity, we gauge-fix to proper-time coordinates and perform a non-perturbative ``Wick rotation'' on the physical configuration space. Under certain assumptions about the behaviour of the partition function under renormalization, we find that the divergence due to the conformal modes of the metric is cancelled non-perturbatively by a Faddeev-Popov determinant contributing to the effective measure. We illustrate some of our claims by a 3d perturbative calculation.