Fractal space-times under the microscope: A Renormalization Group view on Monte Carlo data

TL;DR

This paper investigates the fractal nature of space-time in quantum gravity using renormalization group methods, revealing three scaling regimes and matching Monte Carlo simulation data for spectral dimensions.

Contribution

It provides a detailed RG analysis of spectral and walk dimensions in asymptotically safe quantum gravity, identifying three key scaling regimes and explaining discrepancies in short-distance spectral dimension data.

Findings

Identifies three distinct scaling regimes for space-time dimensions.

Shows good agreement between RG predictions and Monte Carlo simulation data.

Offers an explanation for differences observed in spectral dimensions across quantum gravity approaches.

Abstract

The emergence of fractal features in the microscopic structure of space-time is a common theme in many approaches to quantum gravity. In this work we carry out a detailed renormalization group study of the spectral dimension $d_s$ and walk dimension $d_w$ associated with the effective space-times of asymptotically safe Quantum Einstein Gravity (QEG). We discover three scaling regimes where these generalized dimensions are approximately constant for an extended range of length scales: a classical regime where $d_s = d, d_w = 2$, a semi-classical regime where $d_s = 2d/(2+d), d_w = 2+d$, and the UV-fixed point regime where $d_s = d/2, d_w = 4$. On the length scales covered by three-dimensional Monte Carlo simulations, the resulting spectral dimension is shown to be in very good agreement with the data. This comparison also provides a natural explanation for the apparent puzzle between the short distance behavior of the spectral dimension reported from Causal Dynamical Triangulations (CDT), Euclidean Dynamical Triangulations (EDT), and Asymptotic Safety.