On the relation between Euclidean and Lorentzian 2D quantum gravity

TL;DR

This paper demonstrates that 2D Lorentzian quantum gravity can be derived from Euclidean quantum gravity by removing baby universes, establishing a direct relationship between their geometries and propagators.

Contribution

It provides an explicit method to relate Euclidean and Lorentzian 2D quantum gravity through a peeling procedure and parameter space mapping.

Findings

Lorentzian quantum gravity is a renormalized version of Euclidean quantum gravity.

A peeling procedure links Euclidean and Lorentzian geometries.

Propagators of both theories are identified under a parameter map.

Abstract

Starting from 2D Euclidean quantum gravity, we show that one recovers 2D Lorentzian quantum gravity by removing all baby universes. Using a peeling procedure to decompose the discrete, triangulated geometries along a one-dimensional path, we explicitly associate with each Euclidean space-time a (generalized) Lorentzian space-time. This motivates a map between the parameter spaces of the two theories, under which their propagators get identified. In two dimensions, Lorentzian quantum gravity can therefore be viewed as a ``renormalized'' version of Euclidean quantum gravity.