# Group Field Theory and Holographic Tensor Networks: Dynamical Corrections to the Ryu-Takayanagi formula

## TL;DR

This paper introduces group field theory networks as a new framework for analyzing entanglement entropy in quantum gravity, demonstrating that the Ryu-Takayanagi formula holds with negligible corrections for certain models.

## Contribution

It generalizes spin and tensor networks using group field theory and provides a statistical method to compute entanglement entropy, including proof of negligible corrections in simple models.

## Key findings

- Entanglement entropy follows the Ryu-Takayanagi formula.
- Linear corrections are negligible for broad classes of networks.
- The approach unifies tensor network methods with group field theory.

## Abstract

We introduce group field theory networks as a generalization of spin networks and of (symmetric) random tensor networks and provide a statistical computation of the R\'enyi entropy for a bipartite network state using the partition function of a simple interacting group field theory. The expectation value of the entanglement entropy is calculated by an expansion into stranded Feynman graphs and is shown to be captured by a Ryu- Takayanagi formula. For a simple interacting group field theory, we can prove the linear corrections, given by a polynomial perturbation of the Gaussian measure, to be negligible for a broad class of networks.