On the relation between Euclidean and Lorentzian 2D quantum gravity

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.

12 pages, 2 figures

References in corpus (1)

• Integrable 2D Lorentzian Gravity and Random Walks

Cited by in corpus (39)

• Nonperturbative Quantum Gravity
• Dynamically Triangulating Lorentzian Quantum Gravity
• The Universe from Scratch
• Non-perturbative 3d Lorentzian Quantum Gravity
• Quantizing Horava-Lifshitz Gravity via Causal Dynamical Triangulations
• Discrete Lorentzian Quantum Gravity
• A String Field Theory based on Causal Dynamical Triangulations
• 2d CDT is 2d Horava-Lifshitz quantum gravity
• Quantum Gravity via Causal Dynamical Triangulations
• The Emergence of Spacetime, or, Quantum Gravity on Your Desktop
• A new continuum limit of matrix models
• Putting a cap on causality violations in CDT
• (2+1)-Dimensional Quantum Gravity as the Continuum Limit of Causal Dynamical Triangulations
• The quantum physics of chronology protection
• The emergence of background geometry from quantum fluctuations
• Renormalization of 3d quantum gravity from matrix models
• New multicritical matrix models and multicritical 2d CDT
• Generalized Lorentzian Triangulations and the Calogero Hamiltonian
• The transfer matrix in four-dimensional CDT
• A discrete history of the Lorentzian path integral
• Taming the cosmological constant in 2D causal quantum gravity with topology change
• Pseudo-topological transitions in 2D gravity models coupled to massless scalar fields
• The Geometry of ZZ-branes
• Quantum Gravity on the computer: Impressions of a workshop
• Locally Causal Dynamical Triangulations in Two Dimensions
• Baby Universes Revisited
• Quantum Flatness in Two-Dimensional CDT Quantum Gravity
• A causal perspective on random geometry
• The Real Wick Rotations in Quantum Gravity
• Universality of 2d causal dynamical triangulations
• Measuring the Homogeneity (or Otherwise) of the Quantum Universe
• 3D Lorentzian Quantum Gravity from the asymmetric ABAB matrix model
• Dynamical N-body Equlibrium in Circular Dilaton Gravity
• The nature of ZZ branes
• World-sheet dynamics of ZZ branes
• Space-time foam in 2D and the sum over topologies
• Aspects of quantum gravity
• Making the case for causal dynamical triangulations
• Topology Change and the Emergence of Geometry in Two Dimensional Causal Quantum Gravity