Spectral dimension flow on continuum random multigraph

TL;DR

This paper reviews a multigraph ensemble model that effectively approximates causal dynamical triangulations, capturing key physical properties and elucidating the relationship between spectral and Hausdorff dimensions in quantum gravity.

Contribution

It introduces and advocates for the multigraph ensemble as a suitable analytical tool for studying spectral dimension flow in quantum gravity models.

Findings

Multigraph models effectively reproduce spectral dimension reduction.

The approach links spectral and Hausdorff dimensions.

Analytical computations align with numerical CDT results.

Abstract

We review a recently introduced effective graph approximation of causal dynamical triangulations (CDT), the multigraph ensemble. We argue that it is well suited for analytical computations and that it captures the physical degrees of freedom which are important for the reduction of the spectral dimension as observed in numerical simulations of CDT. In addition multigraph models allow us to study the relationship between the spectral dimension and the Hausdorff dimension, thus establishing a link to other approaches to quantum gravity