Aspects of dynamical dimensional reduction in multigraph ensembles of CDT

TL;DR

This paper investigates a simplified multigraph model of Causal Dynamical Triangulations to understand the observed dimensional reduction in quantum gravity, comparing theoretical properties with numerical simulations across multiple dimensions.

Contribution

It introduces and analyzes multigraph ensembles as effective toy models for studying dimensional reduction in four-dimensional CDT, linking them to Horava-Lifshitz gravity features.

Findings

Multigraph ensembles replicate key features of dimensional reduction in CDT.

The properties of these models align with numerical simulations in 2, 3, and 4 dimensions.

Connections are drawn between CDT and Horava-Lifshitz gravity.

Abstract

We study the continuum limit of a "radially reduced" approximation of Causal Dynamical Triangulations (CDT), so-called multigraph ensembles, and explain why they serve as realistic toy models to study the dimensional reduction observed in numerical simulations of four-dimensional CDT. We present properties of this approximation in two, three and four dimensions comparing them with the numerical simulations and pointing out some common features with 2+1 dimensional Horava-Lifshitz gravity.