Sum over topologies and double-scaling limit in 2D Lorentzian quantum gravity

TL;DR

This paper develops a non-perturbative path integral for 2D Lorentzian quantum gravity that sums over geometries and topologies, avoiding causality violations and achieving a well-defined double-scaling limit.

Contribution

It introduces a Lorentzian structure to exclude causality-violating geometries, enabling an analytical sum with a unique double-scaling limit in 2D quantum gravity.

Findings

Sum over topologies can be performed analytically.

Achieves a well-defined double-scaling limit.

Excludes geometries with large causality violations.

Abstract

We construct a combined non-perturbative path integral over geometries and topologies for two-dimensional Lorentzian quantum gravity. The Lorentzian structure is used in an essential way to exclude geometries with unacceptably large causality violations. The remaining sum can be performed analytically and possesses a unique and well-defined double-scaling limit, a property which has eluded similar models of Euclidean quantum gravity in the past.