Group Field theory and Tensor Networks: towards a Ryu-Takayanagi formula in full quantum gravity

TL;DR

This paper connects group field theory with tensor networks to derive the Ryu-Takayanagi formula for entanglement entropy in quantum gravity, using a novel dictionary and two approximation methods.

Contribution

It introduces a new correspondence between group field theory states and tensor networks, enabling the derivation of the Ryu-Takayanagi formula in quantum gravity.

Findings

Successfully derived the Ryu-Takayanagi formula in two approximation regimes

Established a dictionary linking group field theory and tensor networks

Demonstrated the applicability of tensor network techniques in quantum gravity contexts

Abstract

We establish a dictionary between group field theory (thus, spin networks and random tensors) states and generalized random tensor networks. Then, we use this dictionary to compute the R\'{e}nyi entropy of such states and recover the Ryu-Takayanagi formula, in two different cases corresponding to two different truncations/approximations, suggested by the established correspondence.