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

Dasgupta, Arundhati; Loll, Renate

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

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Dasgupta, Arundhati
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

Loll, Renate
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Dasgupta, A., & Loll, R. (2001). A proper-time cure for the conformal sickness in quantum gravity. Nuclear Physics B, 606, 357-379.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-55C6-C

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.