Group Field theory and Tensor Networks: towards a Ryu-Takayanagi formula in full quantum gravity
General Relativity and Quantum Cosmology
2018-05-16 v3 Statistical Mechanics
High Energy Physics - Theory
Quantum Physics
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.
Keywords
Cite
@article{arxiv.1701.01383,
title = {Group Field theory and Tensor Networks: towards a Ryu-Takayanagi formula in full quantum gravity},
author = {Goffredo Chirco and Daniele Oriti and Mingyi Zhang},
journal= {arXiv preprint arXiv:1701.01383},
year = {2018}
}
Comments
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