Fractal Structure of Loop Quantum Gravity

TL;DR

This paper investigates the fractal properties of space and spacetime in loop quantum gravity, revealing a scale-dependent spectral dimension that transitions from 2 to 3 in space and remains 2 at high energies in spacetime, aligning with other quantum gravity approaches.

Contribution

It provides a novel calculation of the spectral dimension in LQG using the area spectrum, showing a scale-dependent transition in dimensions consistent with other models.

Findings

Spectral dimension of space runs from 2 to 3 across a 1.5 phase transition.

Space-time spectral dimension remains 2 at high energies.

Results align with causal dynamical triangulation and asymptotic safety approaches.

Abstract

In this paper we have calculated the spectral dimension of loop quantum gravity (LQG) using simple arguments coming from the area spectrum at different length scales. We have obtained that the spectral dimension of the spatial section runs from 2 to 3, across a 1.5 phase, when the energy of a probe scalar field decrees from high to low energy. We have calculated the spectral dimension of the space-time also using results from spin-foam models, obtaining a 2-dimensional effective manifold at hight energy. Our result is consistent with other two approach to non perturbative quantum gravity: causal dynamical triangulation and asymptotic safety quantum gravity.