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arXiv:2507.18435 · Physical review. D/Physical review. D.

Surface growth scheme for bulk reconstruction and T T ¯ deformation

Hao-Chun Liang, Jia-Rui Sun, Yuan Sun

Published Sep 8, 2026• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/jljb-lbby

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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.
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 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.
Abstract Tensor networks are used to describe the ground state wavefunction of the quantum many-body system. Recently, it has been shown that a tensor network can generate the anti-de Sitter (AdS) geometry by using the entanglement renormalization approach, which provides a new way to realize bulk reconstruction in the AdS/conformal field theory correspondence. However, whether the dynamical connections can be found between the tensor network and gravity is an important unsolved problem. In this paper, we give a novel proposal to integrate ideas from tensor networks, entanglement entropy, canonical quantization of quantum gravity and the holographic principle and argue that the gravitational dynamics can be generated from a tensor network if the wave function of the latter satisfies the Wheeler–DeWitt equation.
In recent years, the holographic duality between T T ¯ -deformed conformal field theory (CFT) and Anti-de Sitter (AdS) spacetime with finite radial cutoff has received significant attention. The study of T T ¯ deformation within the framework of de Sitter (dS)/CFT duality has also progressed. This paper shows that the trace flow equation in dS spacetime can be analytically extended from its AdS counterpart through double Wick rotations. Meanwhile, we generalize the replica method in both AdS and dS holography to derive a general expression for the entanglement entropy of arbitrary single spatial intervals within the T T ¯ -deformed framework. For both finite size and finite temperature systems, we obtain the analytical expression for the entanglement entropy after T T ¯ deformation. Finally, in dS/dS holography and half-dS holography, we find that the dual field theory exhibits nonlocality by analyzing the strong subadditivity and boosted strong subadditivity of entanglement entropy.
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.
This thesis is devoted to a possible generalization of the entanglement entropy and its implication to the holography, especially AdS/CFT correspondence.The AdS/CFT correspondence is a way to define the quantum gravity in d + 1-dimensional asymptotically anti-de Sitter (AdS) spacetime by using the conformal field theory (CFT) in d-dimension.In this context, it is still unclear how we can realize the d + 1-dimensional full bulk geometries from the d-dimensional quantum field theories.The main object of this thesis is the minimal surface not necessarily anchored on the boundary, which has not been derived from the field theory analysis.First, we review how we can obtain minimal surfaces anchored on the boundary from the entanglement entropy.Then, we introduce a generalization of the entanglement entropy for mixed states and discuss its basic properties.Finally, we argue that we can extract the aforementioned minimal surfaces ending on the bulk from the generalized version of the entanglement entropy.Our explicit derivations include the geometries in three-dimensional AdS and BTZ black holes.First and foremost, I would like to express my deepest gratitude to Norihiro Iizuka, my supervisor.I could not reach here without his patient guidance and encouragement.