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Multiboundary Wormholes and Holographic Entanglement

Balasubramanian, V.; Hayden, P.; Maloney, A.; Marolf, D.; Ross, S.F.

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V. Balasubramanian

P. Hayden

A. Maloney

D. Marolf


The AdS/CFT correspondence relates quantum entanglement between boundary conformal field theories and geometric connections in the dual asymptotically anti-de Sitter spacetime. We consider entangled states in the $n$-fold tensor product of a 1 + 1 dimensional CFT Hilbert space defined by the Euclidean path integral over a Riemann surface with n holes. In one region of moduli space, the dual bulk state is a black hole with n asymptotically AdS3 regions connected by a common wormhole, while in other regions the bulk fragments into disconnected components. We study the entanglement structure and compute the wave function explicitly in the puncture limit of the Riemann surface in terms of CFT n-point functions. We also use AdS minimal surfaces to measure entanglement more generally. In some regions of the moduli space the entanglement is entirely multipartite, though not of the GHZ type. However, even when the bulk is completely connected, there are regions of the moduli space in which the entanglement is instead almost entirely bipartite: significant entanglement occurs only between pairs of CFTs. We develop new tools to analyze intrinsically n-partite entanglement, and use these to show that for some wormholes with n similar sized horizons there is intrinsic entanglement between all n parties, and that the distillable entanglement between the asymptotic regions is at least $(n+1)/2$ partite.


Balasubramanian, V., Hayden, P., Maloney, A., Marolf, D., & Ross, S. (2014). Multiboundary Wormholes and Holographic Entanglement. Classical and Quantum Gravity, 31(18), Article 185015.

Journal Article Type Article
Acceptance Date Aug 4, 2014
Online Publication Date Sep 5, 2014
Publication Date Sep 21, 2014
Deposit Date Oct 3, 2014
Publicly Available Date Oct 6, 2014
Journal Classical and Quantum Gravity
Print ISSN 0264-9381
Electronic ISSN 1361-6382
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 31
Issue 18
Article Number 185015
Keywords Holography, Entanglement, Black holes.


Accepted Journal Article (919 Kb)

Copyright Statement
© 2014 IOP Publishing Ltd. This is an author-created, un-copyedited version of an article accepted for publication in Classical and quantum gravity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at

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