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arXiv · 1612.09533

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

Dario Benedetti·James P. Ryan
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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 Ho\v{r}ava-Lifshitz type, our result strengthens the link between CDT and Ho\v{r}ava-Lifshitz gravity.

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Dario Benedetti, James P. Ryan. 2016-12-30. Capturing the phase diagram of (2+1)-dimensional CDT using a balls-in-boxes model. https://doi.org/10.1088/1361-6382/aa6b5d

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