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

Authors :: Arundhati Dasgupta
Renate Loll
Source :: Nuclear Physics B
Publication Year :: 2001
Publisher :: Elsevier BV, 2001.
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.<br />25 pages, 1 postscript figure; version to appear in Nucl. Phys. B with an added reference and a comment