Capturing the phase diagram of (2+1)-dimensional CDT using a balls-in-boxes model

Abstract

We study the phase diagram of a one-dimensional balls-in-boxes (BIB) model that has been proposed as an effective model for the spatial-volume dynamics of (2+1)-dimensional causal dynamical triangulations (CDT). The latter is a statistical model of random geometries and a candidate for a nonperturbative formulation of quantum gravity, and it is known to have an interesting phase diagram, in particular including a phase of extended geometry with classical properties. Our results corroborate a previous analysis suggesting that a particular type of potential is needed in the BIB model in order to reproduce the droplet condensation typical of the extended phase of CDT. Since such a potential can be obtained by a minisuperspace reduction of a (2+1)-dimensional gravity theory of the Hořava-Lifshitz type, our result strengthens the link between CDT and Hořava-Lifshitz gravity.

21 pages, 7 figures

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• Quantum Gravity from Causal Dynamical Triangulations: A Review
• The phase diagram of the multi-matrix model with ABAB-interaction from functional renormalization
• 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, Hydrodynamics and Emergent Cosmology: A Collection of Perspectives
• CDT and Horava-Lifshitz QG in Two Dimensions
• Yang-Lee zeros for real-space condensation
• Landau Theory of Causal Dynamical Triangulations