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arXiv · 1903.07344

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

Goffredo Chirco·Alex Goeßmann·Daniele Oriti·Mingyi Zhang
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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.

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Goffredo Chirco, Alex Goeßmann, Daniele Oriti, Mingyi Zhang. 2019-03-18. Group Field Theory and Holographic Tensor Networks: Dynamical Corrections to the Ryu-Takayanagi formula. https://doi.org/10.1088/1361-6382%2Fab7bb9

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