Finite Entanglement Entropy in Asymptotically Safe Quantum Gravity

TL;DR

This paper shows that in asymptotically safe quantum gravity, entanglement entropy remains finite and free from divergences, unlike in classical quantum field theory, due to the quantum nature of spacetime.

Contribution

It demonstrates that entanglement entropy in asymptotic safety quantum gravity is finite, resolving divergence issues present in classical approaches.

Findings

Entanglement entropy is free from ultraviolet divergences in asymptotic safety.

Classical spacetime idealization causes artificial divergences.

Quantum spacetime dynamics regularize entanglement entropy.

Abstract

Entanglement entropies calculated in the framework of quantum field theory on classical, flat or curved, spacetimes are known to show an intriguing area law in four dimensions, but they are also notorious for their quadratic ultraviolet divergences. In this paper we demonstrate that the analogous entanglement entropies when computed within the Asymptotic Safety approach to background independent quantum gravity are perfectly free from such divergences. We argue that the divergences are an artifact due to the over-idealization of a rigid, classical spacetime geometry which is insensitive to the quantum dynamics.