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

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Chirco,  Goffredo
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Oriti,  Daniele
Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

Zhang,  Mingyi
AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1903.07344.pdf
(Preprint), 879KB

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Citation

Chirco, G., Goeßmann, A., Oriti, D., & Zhang, M. (2020). Group Field Theory and Holographic Tensor Networks: Dynamical Corrections to the Ryu-Takayanagi formula. Classical and Quantum Gravity, 37(9): 095011. doi:10.1088/1361-6382/ab7bb9.


Cite as: http://hdl.handle.net/21.11116/0000-0003-4D80-6
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.