Coarse graining dynamical triangulations: a new scheme

TL;DR

This paper introduces a novel coarse-graining scheme for dynamical triangulations that aids in understanding large-scale observables and offers a potential new renormalisation approach for quantum gravity.

Contribution

It presents a new coarse-graining procedure for dynamical triangulations, extending ideas from random Delaunay triangulations, aimed at large-scale property preservation and quantum gravity applications.

Findings

Provides a method to define large-scale observables like average scalar curvature.

Suggests the scheme could serve as a basis for a new renormalisation procedure.

Discusses the theoretical advantages and potential applications of the scheme.

Abstract

A new procedure for coarse-graining dynamical triangulations is presented. The procedure provides a meaning for the relevant value of observables when "probing at large scales", e.g. the average scalar curvature. The scheme may also be useful as a starting point for a new type of renormalisation procedure, suitable for dynamically triangulated quantum gravity. Random Delaunay triangulations have previously been used to produce discretisations of continuous Euclidean manifolds, and the coarse-graining scheme is an extension of this idea, using random simplicial complexes produced from a dynamical triangulation. In order for a coarse-graining process to be useful, it should preserve the properties of the original dynamical triangulation that are relevant when probing at large scales. Some general discussion of this point is given, along with some arguments in favour of the proposed scheme.