Entanglement entropy of physical states in hypercuboidally truncated spin foam quantum gravity

TL;DR

This paper investigates the entanglement entropy of physical states in a hypercuboidal truncation of spin foam quantum gravity, revealing its dependence on coupling constants and a maximum near the non-Gaussian fixed point, linked to symmetry restoration.

Contribution

It introduces a numerical analysis of entanglement entropy in hypercuboidal spin foam states and explores its relation to the RG flow fixed point and symmetry restoration.

Findings

Entanglement entropy depends on the theory's coupling constants.

A maximum of EE appears near the non-Gaussian fixed point.

EE behavior is related to the restoration of diffeomorphism symmetry.

Abstract

In this article we consider physical states in the hypercuboidal truncation of the EPRL-FK spin foam quantum gravity model. In particular, these states are defined on graphs which allow considering the entanglement entropy (EE) associated to the bipartition of space. We compute the EE numerically for some examples, and find that it depends on the coupling constants within the theory. We also find that there appears a maximum of the EE within the region of the coupling constant containing the non-Gaussian fixed point of the RG flow of the truncated model. We discuss the relation of this behaviour with the restoration of diffeomorphism symmetry at the fixed point.