It from ETH: Multi-interval Entanglement and Replica Wormholes from Large-$c$ BCFT Ensemble

TL;DR

This paper derives the Ryu-Takayanagi formula directly from 2D CFTs using large-$c$ conformal data, revealing how bulk geometries and multi-boundary black holes emerge from entangled states and ETH in holographic theories.

Contribution

It introduces a CFT-based derivation of RT formula, multi-interval entanglement entropy, and replica wormholes, connecting bulk spacetime emergence to eigenstate thermalization.

Findings

Derivation of RT formula from CFT in high-temperature regime

Detection of replica wormholes via CFT entanglement structure

Construction of holographic tensor networks capturing entanglement

Abstract

We provide a derivation of the Ryu-Takayanagi (RT) formula in 3D gravity for generic boundary subregion--including RT surface phase transitions--directly from the dual two-dimensional conformal field theory (CFT). Our approach relies on the universal statistics of the algebraic conformal data and the large-$c$ behavior of conformal blocks with Cardy boundaries involved. We observe the emergence of 3D multi-boundary black holes with Karch-Randall branes from entangled states of any number of CFT's with and without Cardy boundaries. The RT formula is obtained directly from the CFT in the high-temperature regime. Two direct applications are: $\textbf{1)}$ A simple derivation of the multi-interval entanglement entropy for the vacuum state of a single CFT; $\textbf{2)}$ A CFT-based detection of the emergence of replica wormholes in the context of entanglement islands and black hole microstate counting. Our framework yields the first holographic random tensor network that faithfully captures the entanglement structure of holographic CFTs. These results imply that bulk spacetime geometries indeed emerge from the eigenstate thermalization hypothesis (ETH) in the dual field theory in the large-$c$ limi--a paradigm we refer to as $\textit{It from ETH}$.