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Journal of High Energy Physics

, 2017:148 | Cite as

Discrete gravity on random tensor network and holographic Rényi entropy

Open Access
Regular Article - Theoretical Physics

Abstract

In this paper we apply the discrete gravity and Regge calculus to tensor networks and Anti-de Sitter/conformal field theory (AdS/CFT) correspondence. We construct the boundary many-body quantum state |Ψ〉 using random tensor networks as the holographic mapping, applied to the Wheeler-deWitt wave function of bulk Euclidean discrete gravity in 3 dimensions. The entanglement Rényi entropy of |Ψ〉 is shown to holographically relate to the on-shell action of Einstein gravity on a branch cover bulk manifold. The resulting Rényi entropy S n of |Ψ〉 approximates with high precision the Rényi entropy of ground state in 2-dimensional conformal field theory (CFT). In particular it reproduces the correct n dependence. Our results develop the framework of realizing the AdS3/CFT2 correspondence on random tensor networks, and provide a new proposal to approximate the CFT ground state.

Keywords

AdS-CFT Correspondence Random Systems Gauge-gravity correspondence Lattice Models of Gravity 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.Institut für QuantengravitationUniversität Erlangen-NürnbergErlangenGermany
  2. 2.Department of PhysicsFlorida Atlantic UniversityBoca RatonU.S.A.
  3. 3.Institute for Interdisciplinary Information SciencesTsinghua UniversityBeijingChina

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