Non-perturbative Lorentzian Quantum Gravity, Causality and Topology Change

TL;DR

This paper develops an exactly solvable non-perturbative lattice model for 2D Lorentzian quantum gravity with causality, revealing differences from continuum approaches but reconciling with matrix models when topology change is included.

Contribution

It introduces a non-perturbative lattice formulation of 2D Lorentzian quantum gravity that can be solved exactly and explores the effects of topology change on its relation to other models.

Findings

Continuum limit matches proper-time gauge quantization of 2D gravity.

Disagrees with matrix models and Liouville theory without topology change.

Agreement with matrix models achieved when allowing topology change.

Abstract

We formulate a non-perturbative lattice model of two-dimensional Lorentzian quantum gravity by performing the path integral over geometries with a causal structure. The model can be solved exactly at the discretized level. Its continuum limit coincides with the theory obtained by quantizing 2d continuum gravity in proper-time gauge, but it disagrees with 2d gravity defined via matrix models or Liouville theory. By allowing topology change of the compact spatial slices (i.e. baby universe creation), one obtains agreement with the matrix models and Liouville theory.