On the UV dimensions of Loop Quantum Gravity

Understand

Planck-scale dynamical dimensional reduction is attracting more and more interest in the quantum-gravity literature since it seems to be a model independent effect.

• However different studies base their results on different concepts of spacetime dimensionality.
• Most of them rely on the \textit{spectral} dimension, others refer to the \textit{Hausdorff} dimension and, very recently, it has been introduced also the \textit{thermal} dimension.
• We here show that all these distinct definitions of dimension give the same outcome in the case of the effective regime of Loop Quantum Gravity (LQG).