(2+1)-Dimensional Quantum Gravity as the Continuum Limit of Causal Dynamical Triangulations

Abstract

We perform a non-perturbative sum over geometries in a (2+1)-dimensional quantum gravity model given in terms of Causal Dynamical Triangulations. Inspired by the concept of triangulations of product type introduced previously, we impose an additional notion of order on the discrete, causal geometries. This simplifies the combinatorial problem of counting geometries just enough to enable us to calculate the transfer matrix between boundary states labelled by the area of the spatial universe, as well as the corresponding quantum Hamiltonian of the continuum theory. This is the first time in dimension larger than two that a Hamiltonian has been derived from such a model by mainly analytical means, and opens the way for a better understanding of scaling and renormalization issues.

38 pages, 13 figures

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Cited by in corpus (24)

• Nonperturbative Quantum Gravity
• The Nonperturbative Quantum de Sitter Universe
• Geometry and field theory in multi-fractional spacetime
• Spectral geometry as a probe of quantum spacetime
• Second- and First-Order Phase Transitions in CDT
• The Emergence of Spacetime, or, Quantum Gravity on Your Desktop
• From dispersion relations to spectral dimension - and back again
• De Sitter Universe from Causal Dynamical Triangulations without Preferred Foliation
• Spacetime condensation in (2+1)-dimensional CDT from a Horava-Lifshitz minisuperspace model
• Imposing causality on a matrix model
• 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
• Gravity as an emergent phenomenon: a GFT perspective
• Exploring Torus Universes in Causal Dynamical Triangulations
• A causal perspective on random geometry
• Capturing the phase diagram of (2+1)-dimensional CDT using a balls-in-boxes model
• The phase structure and effective action of 3D CDT at higher spatial genus
• On the Nature of Spatial Universes in 3D Lorentzian Quantum Gravity
• Quantum Gravity from Simplices: Analytical Investigations of Causal Dynamical Triangulations
• Coloured Hard-Dimers
• Next steps in understanding the asymptotics of $3d$ quantum gravity
• A noncommutative enumeration problem
• Central Limit Theorem for Coloured Hard-Dimers
• Landau Theory of Causal Dynamical Triangulations