Entanglement entropy, scale-dependent dimensions and the origin of gravity

TL;DR

This paper explores how the finiteness of entanglement entropy across boundaries relates to the scale-dependent spectral dimension in quantum gravity, suggesting that quantum geometric effects influence gravitational dynamics and may have observable implications.

Contribution

It establishes a connection between finite entanglement entropy and the running spectral dimension, highlighting quantum geometry's role in the emergence of gravity.

Findings

Finite entanglement entropy relates to the vanishing spectral dimension at certain scales.

Quantum geometry's structure affects diffusion processes and entropy behavior.

Running spectral dimension may serve as an observable signature of quantum gravity.

Abstract

We argue that the requirement of a finite entanglement entropy of quantum degrees of freedom across a boundary surface is closely related to the phenomenon of running spectral dimension, universal in approaches to quantum gravity. If quantum geometry hinders diffusion, for instance when its structure at some given scale is discrete or too rough, then the spectral dimension of spacetime vanishes at that scale and the entropy density blows up. A finite entanglement entropy is a key ingredient in deriving Einstein gravity in a semi-classical regime of a quantum-gravitational theory and, thus, our arguments strengthen the role of running dimensionality as an imprint of quantum geometry with potentially observable consequences.