Quantum Einstein Gravity

TL;DR

This paper introduces the Asymptotic Safety approach in Quantum Einstein Gravity, highlighting evidence for a non-trivial fixed point and exploring the fractal nature of quantum space-times through theoretical and numerical comparisons.

Contribution

It provides a pedagogical overview of the Asymptotic Safety program and compares continuum predictions with Monte Carlo data, advancing understanding of quantum space-time structure.

Findings

Evidence supporting a non-trivial renormalization group fixed point

Comparison of spectral dimension predictions with Monte Carlo data

Multifractal structure of quantum space-times

Abstract

We give a pedagogical introduction to the basic ideas and concepts of the Asymptotic Safety program in Quantum Einstein Gravity. Using the continuum approach based upon the effective average action, we summarize the state of the art of the field with a particular focus on the evidence supporting the existence of the non-trivial renormalization group fixed point at the heart of the construction. As an application, the multifractal structure of the emerging space-times is discussed in detail. In particular, we compare the continuum prediction for their spectral dimension with Monte Carlo data from the Causal Dynamical Triangulation approach.