Surface growth scheme for bulk reconstruction and tensor network
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Springer
Received: October 9, Revised: October 25, Accepted: October 29, Published: December 11,
2020 2020 2020 2020
Yi-Yu Lin, Jia-Rui Sun and Yuan Sun School of Physics and Astronomy, Sun Yat-Sen University, Guangzhou 510275, China
E-mail: [email protected], [email protected], [email protected] Abstract: We propose a surface growth approach to reconstruct the bulk spacetime geometry, motivated by Huygens’ principle of wave propagation. We show that our formalism can be explicitly realized with the help of the surface/state correspondence and the one-shot entanglement distillation (OSED) method. We first construct a tensor network corresponding to a special surface growth picture with spherical symmetry and fractal feature using the OSED method and show that the resulting tensor network can be identified with the MERA-like tensor network, which gives a proof that the MERA-like tensor network is indeed a discretized version of the time slice of AdS spacetime, rather than just an analogy. Furthermore, we generalize the original OSED method to describe more general surface growth picture by using of the surface/state correspondence and the generalized RT formula, which leads to a more profound interpretation for the surface growth process and provides a concrete and intuitive way for the idea of entanglement wedge reconstruction. Keywords: AdS-CFT Correspondence, Gauge-gravity correspondence, Models of Quantum Gravity ArXiv ePrint: 2010.01907
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP12(2020)083
JHEP12(2020)083
Surface growth scheme for bulk reconstruction and tensor network
Contents 1 Introduction
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2 Introduction to surface growth scheme
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3 Constructing the tensor network
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5 More general surface growth scheme
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6 Conclusions and discussions
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1
Introduction
The anti-de Sitter/conformal field theory (AdS/CFT) correspondence and the general gauge/gravity duality not only provide powerful tools for studying strongly coupled quantum field theories, but also provide new perspectives for studying quantum gravity, in which the quantum field theory on the boundary is viewed as the quantum gravity description of the dual bulk gravity, instead of quantizing the gravity directly [1–3]. To fully understand the duality between the bulk and the boundary, it is important to study how the bulk gravitational theory can be constructed from the boundary quantum field theory, this formalism is called the bulk reconstruction [15–22]. It has been shown that the notion of quantum entanglement, especially the holographic description of entanglement entropy, i.e. the holographic entanglement entropy, plays an essential role in the bulk reconstruction. It was proposed by Ryu and Takayanagi (RT) and later generalized by Hubeny, Rangamani and Takayanagi (HRT) that the entanglement entropy of a boundary subregion A of a CFT is given by [4–6] Area (γA ) SA = , (1.1) 4G where γA is the codimension-two bulk minimal surface which anchored on the boundary
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