Ryu-Takayanagi Formula for Multi-Boundary Black Holes from 2D Large-$c$ CFT Ensemble
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arXiv
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| Natura: | Preprint |
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2025
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| author | Bao, Ning Geng, Hao Jiang, Yikun |
| author_facet | Bao, Ning Geng, Hao Jiang, Yikun |
| contents | We study a class of quantum states involving multiple entangled CFTs in AdS$_3$/CFT$_2$, associated with multi-boundary black hole geometries, and demonstrate that the Ryu-Takayanagi (RT) formula for entanglement entropy can be derived using only boundary CFT data. Approximating the OPE coefficients by their Gaussian moments within the 2D large-$c$ CFT ensemble, we show that both the norm of the states and the entanglement entropies associated with various bipartitions--reproducing the expected bulk dual results--can be computed purely from the CFT. All $\textit{macroscopic geometric}$ structures arising from gravitational saddles emerge entirely from the universal statistical moments of the $\textit{microscopic algebraic}$ CFT data, revealing a statistical-mechanical mechanism underlying semiclassical gravity. We establish a precise correspondence between the CFT norm, the Liouville partition function with ZZ boundary conditions, and the exact gravitational path integral over 3D multi-boundary black hole geometries. For entanglement entropy, each RT phase arises from a distinct leading-order Gaussian contraction, with phase transitions--analogous to replica wormholes--emerging naturally from varying dominant statistical patterns in the CFT ensemble. Our derivation elucidates how the general mechanism behind holographic entropy, namely a boundary replica direction that elongates and becomes contractible in the bulk dual, is encoded explicitly in the statistical structure of the CFT data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12388 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ryu-Takayanagi Formula for Multi-Boundary Black Holes from 2D Large-$c$ CFT Ensemble Bao, Ning Geng, Hao Jiang, Yikun High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics Quantum Physics We study a class of quantum states involving multiple entangled CFTs in AdS$_3$/CFT$_2$, associated with multi-boundary black hole geometries, and demonstrate that the Ryu-Takayanagi (RT) formula for entanglement entropy can be derived using only boundary CFT data. Approximating the OPE coefficients by their Gaussian moments within the 2D large-$c$ CFT ensemble, we show that both the norm of the states and the entanglement entropies associated with various bipartitions--reproducing the expected bulk dual results--can be computed purely from the CFT. All $\textit{macroscopic geometric}$ structures arising from gravitational saddles emerge entirely from the universal statistical moments of the $\textit{microscopic algebraic}$ CFT data, revealing a statistical-mechanical mechanism underlying semiclassical gravity. We establish a precise correspondence between the CFT norm, the Liouville partition function with ZZ boundary conditions, and the exact gravitational path integral over 3D multi-boundary black hole geometries. For entanglement entropy, each RT phase arises from a distinct leading-order Gaussian contraction, with phase transitions--analogous to replica wormholes--emerging naturally from varying dominant statistical patterns in the CFT ensemble. Our derivation elucidates how the general mechanism behind holographic entropy, namely a boundary replica direction that elongates and becomes contractible in the bulk dual, is encoded explicitly in the statistical structure of the CFT data. |
| title | Ryu-Takayanagi Formula for Multi-Boundary Black Holes from 2D Large-$c$ CFT Ensemble |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2504.12388 |