Trees and spatial topology change in CDT

Jan Ambjorn; Timothy George Budd

doi:10.1088/1751-8113/46/31/315201

Trees and spatial topology change in CDT

Jan Ambjorn, Timothy George Budd

Theoretical high energy, astroparticle and gravitational physics

34 Citations (Scopus)

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.

Original language	Undefined/Unknown
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	46
Issue number	31
ISSN	1751-8113
DOIs	https://doi.org/10.1088/1751-8113/46/31/315201
Publication status	Published - 19 Jul 2013

Keywords

hep-th
gr-qc
math-ph
math.CO
math.MP

Access to Document

10.1088/1751-8113/46/31/315201

Cite this

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N2 - 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.

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