A Lorentzian cure for Euclidean troubles

TL;DR

This paper argues that conformal-factor divergences plaguing Euclidean quantum gravity path integrals are mitigated in a non-perturbative Lorentzian framework. By formulating gravity via Lorentzian dynamical triangulations and performing a non-perturbative Wick rotation, the resulting Euclidean action becomes bounded and the path integral converges, with evidence that Lorentzian DT differs from Euclidean DT in higher dimensions. The conformal mode is shown to be non-propagating due to a cancellation between the kinetic term and the path-integral measure, a result supported by both discrete (bounded action and entropic suppression) and continuum (Faddeev-Popov measure) analyses. In 2+1D toy models, the continuum limit requires sufficient entropy from interpolating geometries, underscoring the importance of entropy in achieving a well-defined quantum gravity theory. Overall, the findings bolster Lorentzian dynamical triangulations as a promising route to a consistent, non-perturbative theory of four-dimensional quantum gravity.

Abstract

There is strong evidence coming from Lorentzian dynamical triangulations that the unboundedness of the gravitational action is no obstacle to the construction of a well-defined non-perturbative path integral. In a continuum approach, a similar suppression of the conformal divergence comes about as the result of a non-trivial path-integral measure.