It from ETH: multi-interval entanglement and replica wormholes from large-c BCFT ensemble
4 affiliations
- 1Harvard University
- 2Tsinghua University
- 3Yanqi Lake Beijing Institute of Mathematical Sciences and Applications (BIMSA)
- 4Northeastern University
Abstract
A bstract We provide a derivation of the Ryu-Takayanagi (RT) formula in 3D gravity for generic boundary subregions — 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 CFTs with and without Cardy boundaries. The RT formula is obtained directly from the CFT in the high-temperature regime. Two direct applications are: 1) A simple derivation of the multi-interval entanglement entropy for the vacuum state of a single CFT; 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 limit — a paradigm we refer to as It from ETH .
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BibTeX
@article{geng2026from,
title = {{It from ETH: multi-interval entanglement and replica wormholes from large-c BCFT ensemble}},
author = {Hao Geng and Ling-Yan Hung and Yikun Jiang},
journal = {Journal of High Energy Physics},
year = {2026},
month = jul,
doi = {10.1007/jhep07(2026)262},
url = {https://doi.org/10.1007/jhep07(2026)262},
note = {CC BY},
}
RIS
TY - JOUR
TI - It from ETH: multi-interval entanglement and replica wormholes from large-c BCFT ensemble
AU - Hao Geng
AU - Ling-Yan Hung
AU - Yikun Jiang
PY - 2026
DA - 2026/07/28
JO - Journal of High Energy Physics
DO - 10.1007/jhep07(2026)262
UR - https://doi.org/10.1007/jhep07(2026)262
AB - A bstract We provide a derivation of the Ryu-Takayanagi (RT) formula in 3D gravity for generic boundary subregions — 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 CFTs with and without Cardy boundaries. The RT formula is obtained directly from the CFT in the high-temperature regime. Two direct applications are: 1) A simple derivation of the multi-interval entanglement entropy for the vacuum state of a single CFT; 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 limit — a paradigm we refer to as It from ETH .
SN - 1029-8479
SN - 1126-6708
SN - 1127-2236
ER -