Coarse-Grained Fixed-Point Tensor Networks and Holographic Reflected Entropy in 3D Gravity
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| Format: | Preprint |
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2025
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| author | Bao, Ning Chu, Jinwei Jiang, Yikun March, Jacob |
| author_facet | Bao, Ning Chu, Jinwei Jiang, Yikun March, Jacob |
| contents | We use the framework of $\textit{fixed-point BCFT tensor networks}$ to present a microscopic CFT derivation of the correspondence between reflected entropy (RE) and entanglement wedge cross section (EW) in AdS$_3$/CFT$_2$, for both bipartite and multipartite settings. These fixed-point tensor networks, obtained by triangulating Euclidean CFT path integrals, allow us to explicitly construct the canonical purification via cutting-and-gluing CFT path integrals. Employing modular flow in the large-$c$ limit, we demonstrate that these intrinsic CFT manipulations reproduce bulk geometric prescriptions, without assuming the AdS/CFT dictionary. The emergence of bulk geometry is traced to coarse-graining over heavy states in the large-$c$ limit. Universal coarse-grained BCFT data for compact 2D CFTs, through the relation to Liouville theory with ZZ boundary conditions, yields hyperbolic geometry on the Cauchy slice. The corresponding averaged replica partition functions reproduce all candidate EWs, arising from different averaging patterns, with the dominant one providing the correct RE and EW. In this way, many heuristic tensor-network intuitions in toy models are made precise and established directly from intrinsic CFT data. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_10170 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Coarse-Grained Fixed-Point Tensor Networks and Holographic Reflected Entropy in 3D Gravity Bao, Ning Chu, Jinwei Jiang, Yikun March, Jacob High Energy Physics - Theory Strongly Correlated Electrons General Relativity and Quantum Cosmology Quantum Physics We use the framework of $\textit{fixed-point BCFT tensor networks}$ to present a microscopic CFT derivation of the correspondence between reflected entropy (RE) and entanglement wedge cross section (EW) in AdS$_3$/CFT$_2$, for both bipartite and multipartite settings. These fixed-point tensor networks, obtained by triangulating Euclidean CFT path integrals, allow us to explicitly construct the canonical purification via cutting-and-gluing CFT path integrals. Employing modular flow in the large-$c$ limit, we demonstrate that these intrinsic CFT manipulations reproduce bulk geometric prescriptions, without assuming the AdS/CFT dictionary. The emergence of bulk geometry is traced to coarse-graining over heavy states in the large-$c$ limit. Universal coarse-grained BCFT data for compact 2D CFTs, through the relation to Liouville theory with ZZ boundary conditions, yields hyperbolic geometry on the Cauchy slice. The corresponding averaged replica partition functions reproduce all candidate EWs, arising from different averaging patterns, with the dominant one providing the correct RE and EW. In this way, many heuristic tensor-network intuitions in toy models are made precise and established directly from intrinsic CFT data. |
| title | Coarse-Grained Fixed-Point Tensor Networks and Holographic Reflected Entropy in 3D Gravity |
| topic | High Energy Physics - Theory Strongly Correlated Electrons General Relativity and Quantum Cosmology Quantum Physics |
| url | https://arxiv.org/abs/2509.10170 |