Trees and spatial topology change in CDT

Abstract

Generalized causal dynamical triangulations (generalized CDT) is a model of two-dimensional quantum gravity in which a limited number of spatial topology changes is allowed to occur. We solve the model at the discretized level using bijections between quadrangulations and trees. In the continuum limit (scaling limit) the amplitudes are shown to agree with known formulas and explicit expressions are obtained for loop propagators and two-point functions. It is shown that from a combinatorial point of view generalized CDT can be viewed as the scaling limit of planar maps with a finite number of faces and we determine the distance function on this ensemble of planar maps. Finally, the relation with planar maps is used to illuminate a mysterious identity of certain continuum cylinder amplitudes.

41 pages, 18 figures. Many details and proofs added

References in corpus (8)

• Nonperturbative Quantum Gravity
• A String Field Theory based on Causal Dynamical Triangulations
• A Matrix Model for 2D Quantum Gravity defined by Causal Dynamical Triangulations
• The three-point function of planar quadrangulations
• New multicritical matrix models and multicritical 2d CDT
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• Wilson Loops in 2D Noncommutative Euclidean Gauge Theory: 2. 1/θExpansion

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• Wormholes, a fluctuating cosmological constant and the Coleman mechanism
• Models of the Universe based on Jordan algebras
• The microscopic structure of 2D CDT coupled to matter
• A model for emergence of space and time
• On the diameter of random planar graphs
• Scalar fields in Causal Dynamical Triangulations
• Bijective enumeration of planar bipartite maps with three tight boundaries, or how to slice pairs of pants
• On a conjecture by Chapuy about Voronoi cells in large maps
• A restricted dimer model on a 2-dimensional random causal triangulation
• Scale-dependent Hausdorff dimensions in 2d gravity
• The three-point function of general planar maps
• Creating 3, 4, 6 and 10-dimensional spacetime from W3 symmetry
• Criticality at absolute zero from Ising model on two-dimensional dynamical triangulations
• Towards elucidation of zero-temperature criticality of Ising model on 2d DT
• The generating function of planar Eulerian orientations
• CDT and Horava-Lifshitz QG in Two Dimensions
• Branched polymers with loops coupled to the critical Ising model