A Lorentzian path integral contour for charged AdS black holes selects a finite subset of complex saddles via Picard-Lefschetz theory, ensuring the semiclassical sum converges at finite β.
A proper-time cure for the conformal sickness in quantum gravity
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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.
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How to tame your (black hole) saddles: Lessons from the Lorentzian Gravitational Path Integral
A Lorentzian path integral contour for charged AdS black holes selects a finite subset of complex saddles via Picard-Lefschetz theory, ensuring the semiclassical sum converges at finite β.