Fractal Spacetime Structure in Asymptotically Safe Gravity

TL;DR

This paper demonstrates that in asymptotically safe quantum gravity, spacetime exhibits a fractal structure with a spectral dimension of 2 at small scales and 4 at large scales, confirming predictions through an exact, non-truncated analysis.

Contribution

It proves that the spectral dimension of spacetime in asymptotic safety equals 2 microscopically, independently of truncations, linking theoretical predictions with numerical simulations.

Findings

Spectral dimension equals 2 at microscopic scales.

Spectral dimension equals 4 at macroscopic scales.

Result is an exact consequence of asymptotic safety.

Abstract

Four-dimensional Quantum Einstein Gravity (QEG) is likely to be an asymptotically safe theory which is applicable at arbitrarily small distance scales. On sub-Planckian distances it predicts that spacetime is a fractal with an effective dimensionality of 2. The original argument leading to this result was based upon the anomalous dimension of Newton's constant. In the present paper we demonstrate that also the spectral dimension equals 2 microscopically, while it is equal to 4 on macroscopic scales. This result is an exact consequence of asymptotic safety and does not rely on any truncation. Contact is made with recent Monte Carlo simulations.