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| Format: | Preprint |
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2025
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| Online-Zugang: | https://arxiv.org/abs/2512.19452 |
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| _version_ | 1866910233680412672 |
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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 |