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Chirco, Goffredo; Goessmann, Alex; Oriti, Daniele; Zhang, Mingyi (2020): Group field theory and holographic tensor networks: dynamical corrections to the Ryu-Takayanagi formula. In: Classical and Quantum Gravity, Vol. 37, No. 9, 095011
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Abstract

We introduce a generalised class of (symmetric) random tensor network states in the framework of group field theory. In this setting, we compute the Renyi entropy for a generic bipartite state via a mapping to the partition function of a topological 3D BF theory, realised as 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 the simple case of a 3D BF 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.