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

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 Rényi 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.

54 pages, 10 figures; v2: replace figure 1 with a new version. Matches submitted version. v3: remove Renyi entropy computation on the random tensor network, focusing on GFT computation and interpretation