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.
Highlights
Introduction to surface growth schemeThe basic idea of the surface growth proposal is as follows
We first construct a tensor network corresponding to a special surface growth picture with spherical symmetry and fractal feature using the one-shot entanglement distillation (OSED) method and show that the resulting tensor network can be identified with the multiscale entanglement renormalization ansatz (MERA)-like tensor network, which gives a proof that the MERA-like tensor network is a discretized version of the time slice of AdS spacetime, rather than just an analogy
In this paper, inspired by Huygens’ principle of wave propagation, and based on the surface/state correspondence, we proposed an intriguing surface growth scheme for the bulk reconstruction
Summary
The basic idea of the surface growth proposal is as follows. In the present paper we will take the AdS3 spacetime as an example, its metric in the global coordinate is ds2 = dρ2 + L2 − cosh ρ dt2 + sinh ρ dφ , L (2.1). We can demonstrate the rationality of this idea qualitatively at least for the regions near the spacetime boundary as follows: since the minimal surface just extends a small distance in the radial direction away from the boundary, it can be considered that what we do is just taking the boundary cutoff a little larger and regarding the envelope of these minimal surfaces as a new boundary, we are just probing the bulk information at the new boundary. It has been argued that the generalized RT formula still holds in cAdS/dCFT correspondence, in which the area of the extremal surface ending on the cut-off surface measures the holographic entanglement entropy in the T T-deformed CFT [28,29,30,31,32] This is exactly consistent with our qualitative arguement. As will be shown below, we will use the so-called OSED method [33] to implement our surface growth scheme
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