Ryu-Takayanagi Formula for Multi-Boundary Black Holes from 2D Large-\textbf{$c$} CFT Ensemble

• URL: http://arxiv.org/abs/2504.12388v1
• Date: Wed, 16 Apr 2025 18:00:06 GMT
• Title: Ryu-Takayanagi Formula for Multi-Boundary Black Holes from 2D Large-\textbf{$c$} CFT Ensemble
• Authors: Ning Bao, Hao Geng, Yikun Jiang,
• Abstract summary: We study a class of quantum states involving multiple entangled CFTs in AdS$_3$/CFT$$.<n>We demonstrate that the Ryu-Takayanagi (RT) formula for entanglement entropy can be derived using only boundary CFT data.
• Score: 1.8794920644097155
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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