Computer Simulations of 3d Lorentzian Quantum Gravity

Abstract

We investigate the phase diagram of non-perturbative three-dimensional Lorentzian quantum gravity with the help of Monte Carlo simulations. The system has a first-order phase transition at a critical value $k_0^c$ of the bare inverse gravitational coupling constant $k_0$. For $k_0>k_0^c$ the system reduces to a product of uncorrelated Euclidean 2d gravity models and has no intrinsic interest as a model of 3d gravity. For $k_0<k_0^c$, extended three-dimensional geometries dominate the functional integral despite the fact that we perform a sum over geometries and no particular background is distinguished at the outset. Furthermore, all systems with $k_0<k_0^c$ have the same continuum limit. A different choice of $k_0$ corresponds merely to a redefinition of the overall length scale.

4 pages, contribution to Lattice 2000 (Gravity and Matrix Models), typos corrected

References in corpus (3)

• Non-perturbative Lorentzian Quantum Gravity, Causality and Topology Change
• A non-perturbative Lorentzian path integral for gravity
• Non-perturbative 3d Lorentzian Quantum Gravity

Cited by in corpus (12)

• Dynamically Triangulating Lorentzian Quantum Gravity
• Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe
• The Universe from Scratch
• Proper Time Flow Equation for Gravity
• A proper-time cure for the conformal sickness in quantum gravity
• Non-perturbative 3d Lorentzian Quantum Gravity
• Renormalization of 3d quantum gravity from matrix models
• A Hexagon Model for 3D Lorentzian Quantum Cosmology
• A discrete history of the Lorentzian path integral
• The phase structure and effective action of 3D CDT at higher spatial genus
• On the Nature of Spatial Universes in 3D Lorentzian Quantum Gravity
• Matters of Gravity, the newsletter of the APS Topical Group on Gravitation, Spring 2001