Lorentzian 3d Gravity with Wormholes via Matrix Models

Abstract

We uncover a surprising correspondence between a non-perturbative formulation of three-dimensional Lorentzian quantum gravity and a hermitian two-matrix model with ABAB-interaction. The gravitational transfer matrix can be expressed as the logarithm of a two-matrix integral, and we deduce from the known structure of the latter that the model has two phases. In the phase of weak gravity, well-defined two-dimensional universes propagate in proper time, whereas in the strong-coupling phase the spatial hypersurfaces disintegrate into many components connected by wormholes.

35 pages, 9 figures

Cited by in corpus (44)

• Reconstructing the Universe
• Nonperturbative Quantum Gravity
• Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe
• The Nonperturbative Quantum de Sitter Universe
• The Universe from Scratch
• An invitation to loop quantum gravity
• Spectral geometry as a probe of quantum spacetime
• Second- and First-Order Phase Transitions in CDT
• Quantizing Horava-Lifshitz Gravity via Causal Dynamical Triangulations
• A Lorentzian cure for Euclidean troubles
• Counting a black hole in Lorentzian product triangulations
• Spacetime foam: a review
• The quantum physics of chronology protection
• (2+1)-Dimensional Quantum Gravity as the Continuum Limit of Causal Dynamical Triangulations
• Spacetime condensation in (2+1)-dimensional CDT from a Horava-Lifshitz minisuperspace model
• Renormalization of 3d quantum gravity from matrix models
• A Hexagon Model for 3D Lorentzian Quantum Cosmology
• 3d Lorentzian, Dynamically Triangulated Quantum Gravity
• The Complete Barrett-Crane Model and its Causal Structure
• A discrete history of the Lorentzian path integral
• Pseudo-topological transitions in 2D gravity models coupled to massless scalar fields
• A first look at transition amplitudes in (2+1)-dimensional causal dynamical triangulations
• The phase diagram of the multi-matrix model with ABAB-interaction from functional renormalization
• Gauge fixing in Causal Dynamical Triangulations
• Exploring Torus Universes in Causal Dynamical Triangulations
• A quantization of topological M theory
• Capturing the phase diagram of (2+1)-dimensional CDT using a balls-in-boxes model
• Pseudo-Cartesian coordinates in a model of Causal Dynamical Triangulations
• A causal perspective on random geometry
• Expoential bounds on the number of causal triangulations
• Topology induced first-order phase transitions in lattice quantum gravity
• The asymmetric ABAB matrix model
• Path integral and conformal instability in nonlocal quantum gravity
• A statistical formalism of Causal Dynamical Triangulations
• The phase structure and effective action of 3D CDT at higher spatial genus
• The F model on dynamical quadrangulations
• Chirality and Symmetry Breaking in a discrete internal Space
• On the Nature of Spatial Universes in 3D Lorentzian Quantum Gravity
• Comment on "The phase diagram of the multi-matrix model with ABAB-interaction from functional renormalization"
• Matters of Gravity, the newsletter of the APS Topical Group on Gravitation, Spring 2001
• Causal dynamical triangulation of a 3D tensor model
• A ribbon graph derivation of the algebra of functional renormalization for random multi-matrices with multi-trace interactions
• The structure of spatial slices of three-dimensional causal triangulations
• Landau Theory of Causal Dynamical Triangulations