Fractal spacetime from the area spectrum

In this communication, we calculate the spectral dimension in loop quantum gravity (LQG) using simple arguments coming from the area spectrum at different length scales. We obtain 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 decreases from high to low energy. We calculate also the spectral dimension of the spacetime using results from spin-foam models and we obtain a two-dimensional effective manifold at high energy. Our result is consistent with two other approaches to non-perturbative quantum gravity: causal dynamical triangulation and asymptotically safety quantum gravity.