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Hauptverfasser: Wen, Qiang, Xu, Mingshuai, Zhong, Haocheng
Format: Preprint
Veröffentlicht: 2025
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Online-Zugang:https://arxiv.org/abs/2512.19452
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author Wen, Qiang
Xu, Mingshuai
Zhong, Haocheng
author_facet Wen, Qiang
Xu, Mingshuai
Zhong, Haocheng
contents Holographic tensor networks serve as toy models for the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, capturing many of its essential features in a concrete manner. However, existing holographic tensor network models remain far from a complete theory of quantum gravity. A key obstacle is their discrete structure, which only approximates the semi-classical geometry of gravity in a qualitative sense. In \cite{Lin:2024dho}, it was shown that a network of partial-entanglement-entropy (PEE) threads, which are bulk geodesics with a specific density distribution, generates a perfect tessellation of AdS space. Moreover, such PEE-network tessellations can be constructed for more highly symmetric geometries using the Crofton formula. In this paper, we assign a quantum state to each vertex in the PEE network and develop several holographic tensor network models: (1) the factorized PEE tensor network, which takes the form of a tensor product of EPR pairs; (2) the HaPPY-like PEE tensor network constructed from perfect tensors; and (3) the random PEE tensor network. In all these models, we reproduce the exact Ryu-Takayanagi formula by showing that the minimal number of cuts along a homologous surface in the network exactly equals the area of that surface.
format Preprint
id arxiv_https___arxiv_org_abs_2512_19452
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Holographic Tensor Networks as Tessellations of Geometry
Wen, Qiang
Xu, Mingshuai
Zhong, Haocheng
High Energy Physics - Theory
General Relativity and Quantum Cosmology
Quantum Physics
Holographic tensor networks serve as toy models for the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, capturing many of its essential features in a concrete manner. However, existing holographic tensor network models remain far from a complete theory of quantum gravity. A key obstacle is their discrete structure, which only approximates the semi-classical geometry of gravity in a qualitative sense. In \cite{Lin:2024dho}, it was shown that a network of partial-entanglement-entropy (PEE) threads, which are bulk geodesics with a specific density distribution, generates a perfect tessellation of AdS space. Moreover, such PEE-network tessellations can be constructed for more highly symmetric geometries using the Crofton formula. In this paper, we assign a quantum state to each vertex in the PEE network and develop several holographic tensor network models: (1) the factorized PEE tensor network, which takes the form of a tensor product of EPR pairs; (2) the HaPPY-like PEE tensor network constructed from perfect tensors; and (3) the random PEE tensor network. In all these models, we reproduce the exact Ryu-Takayanagi formula by showing that the minimal number of cuts along a homologous surface in the network exactly equals the area of that surface.
title Holographic Tensor Networks as Tessellations of Geometry
topic High Energy Physics - Theory
General Relativity and Quantum Cosmology
Quantum Physics
url https://arxiv.org/abs/2512.19452