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

In this article we consider physical states in the hypercuboidal truncation of the EPRL-FK spin foam model for Euclidean quantum gravity. 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 constant alpha within the theory, which has recently been introduced in the face amplitude. 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.