Ryu-Takayanagi formula for multi-boundary black holes from 2D large-c CFT ensemble

A bstract 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 macroscopic geometric structures arising from gravitational saddles emerge entirely from the universal statistical moments of the 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.