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arXiv:2010.03167 · Chinese Physics C

Note on surface growth approach for bulk reconstruction *

Chao Yu, Fang-Zhong Chen, Yi-Yu Lin, Jia-Rui Sun, Yuan Sun

Published Apr 24, 2022• 7 citations
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Abstract

Abstract In this paper, we show using several examples that the bulk geometry of asymptotically AdS spacetimes can be effectively reconstructed using an intuitive and visual method called the surface growth scheme. This new approach for bulk reconstruction was originally proposed in a recent paper, along with its explicit realization using the one-shot entanglement distillation tensor network and the surface/state correspondence. In this paper, we directly analyze the growth of the bulk minimal surfaces to implement this scheme. Our study provides further support for the surface growth approach in entanglement wedge reconstruction.

DOI
10.1088/1674-1137/ac69ba

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Abstract In this paper, we show using several examples that the bulk geometry of asymptotically AdS spacetimes can be effectively reconstructed using an intuitive and visual method called the surface growth scheme. This new approach for bulk reconstruction was originally proposed in a recent paper, along with its explicit realization using the one-shot entanglement distillation tensor network and the surface/state correspondence. In this paper, we directly analyze the growth of the bulk minimal surfaces to implement this scheme. Our study provides further support for the surface growth approach in entanglement wedge reconstruction.
Abstract In this study, we extend the surface growth approach for bulk reconstruction into the AdS spacetime with a boundary in the AdS/BCFT correspondence. We show that the geometry in the entanglement wedge with a boundary can be constructed from the direct growth of bulk extremal surfaces layer by layer. Furthermore, we observe that the surface growth configuration in BCFT can be connected with the defect multi scale entanglement renormalization ansatz (MERA) tensor network. Additionally, we investigate the entanglement of purification within the surface growth process, which not only reveals more refined structure of entanglement entropy in the entanglement wedge but also suggests a selection rule for surface growth in the bulk reconstruction.
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.
In this paper, we study the dynamical connection between the surface growth scheme and the conformal field theory with T T ¯ deformation. By utilizing the extended one-shot entanglement distillation tensor network, we find that the iterative growth, i.e., radial evolution of homogenous and isotropic bulk minimal surfaces in asymptotically anti–de Sitter spacetime can be mapped to the T T ¯ operator flow driven by the deformation parameter. Our results show that the T T ¯ deformation can provide a dynamical mechanism for the surface growth in asymptotically anti–de Sitter spacetime, which may shed light on reconstructing bulk gravitational dynamics from the surface growth scheme.
In this paper, we extend the surface growth scheme in AdS spacetime with a boundary in the AdS/BCFT correspondence. We show that the entanglement wedge with a boundary can be constructed from the direct growth of bulk extremal surfaces layer by layer. In addition, we find that the surface growth configuration in BCFT can be connected with the defect multi scale entanglement renormalization ansatz (MERA) tensor network. Furthermore, we also investigate the entanglement of purification within the surface growth process, which reveals more refined structure of entanglement entropy and indicates a selection rule for surface growth in the bulk reconstruction.
We propose a novel and natural surface growth approach to reconstruct the bulk spacetime. The picture is similar to Huygens' principle of wave propagation, in which each subregion of the old entanglement surface becomes a ``wave source'' of the new one, then layer by layer, the newly generated entanglement surfaces can reach bulk region far away from the boundary. We show that this picture can be described reasonably and quantitatively, and thus provides a concrete and intuitive way for the entanglement wedge reconstruction.
A bstract In the AdS/CFT correspondence, the causal structure of the bulk AdS spacetime is tied to entanglement in the dual CFT. This relationship is captured by the connected wedge theorem [1], which states that a bulk scattering process implies the existence of O (1/ G N ) entanglement between associated boundary subregions. In this paper, we study the connected wedge theorem in two asymptotically AdS 2+1 spacetimes: the conical defect and BTZ black hole geometries. In these settings, we find that bulk scattering processes require not just large entanglement, but also additional restrictions related to candidate RT surfaces which are non-minimal. We argue these extra relationships imply a certain CFT entanglement structure involving internal degrees of freedom. Because bulk scattering relies on sub-AdS scale physics, this supports the idea that sub-AdS scale locality emerges from internal degrees of freedom. While the new restriction that we identify on non-minimal surfaces is stronger than the initial statement of the connected wedge theorem, we find that it is necessary but still not sufficient to imply bulk scattering in mixed states.