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Group field theory and tensor networks: towards a Ryu-Takayanagi formula in full quantum gravity. (English) Zbl 1393.83015

Summary: 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 S. Ryu and T. Takayanagi[Phys. Rev. Lett. 96, No. 18, Article ID 181602 (2006; doi:10.1103/PhysRevLett.96.181602)] formula, in two different cases corresponding to two different truncations/approximations, suggested by the established correspondence.

MSC:

83C45 Quantization of the gravitational field
62P35 Applications of statistics to physics
81T10 Model quantum field theories
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