Making the gravitational path integral more Lorentzian, or: Life beyond Liouville gravity

TL;DR

This paper explores a Lorentzian quantum gravity theory in two dimensions that differs from Euclidean Liouville gravity, offering a non-fractal geometry, consistency with matter coupling, and potential for higher-dimensional generalizations.

Contribution

It introduces a rigorous Lorentzian path integral for 2D quantum gravity, highlighting its advantages over Euclidean approaches and its broader applicability.

Findings

Quantum geometry is non-fractal

Remains consistent with matter beyond c=1

Generalizes to higher dimensions

Abstract

In two space-time dimensions, there is a theory of Lorentzian quantum gravity which can be defined by a rigorous, non-perturbative path integral and is inequivalent to the well-known theory of (Euclidean) quantum Liouville gravity. It has a number of appealing features: i) its quantum geometry is non-fractal, ii) it remains consistent when coupled to matter, even beyond the c=1 barrier, iii) it is closer to canonical quantization approaches than previous path-integral formulations, and iv) its construction generalizes to higher dimensions.