Arxiv:1406.2663V2 [Hep-Th]
Multiboundary Wormholes and Holographic Entanglement Vijay Balasubramaniana;b, Patrick Haydenc, Alexander Maloneyd;e, Donald Marolff , Simon F. Rossg aDavid Rittenhouse Laboratories, University of Pennsylvania 209 S 33rd Street, Philadelphia, PA 19104, USA bCUNY Graduate Center, Initiative for the Theoretical Sciences 365 Fifth Avenue, New York, NY 10016, USA cDepartment of Physics, Stanford University Palo Alto, CA 94305, USA dDepartment of Physics, McGill University 3600 rue Universit´e,Montreal H3A2T8, Canada eCenter for the Fundamental Laws of Nature, Harvard University Cambridge, MA 02138, USA f Department of Physics, University of California, Santa Barbara, CA 93106, USA gCentre for Particle Theory, Department of Mathematical Sciences Durham University, South Road, Durham DH1 3LE, UK Abstract The AdS/CFT correspondence relates quantum entanglement between boundary Conformal Field Theories and geometric connections in the dual asymptotically Anti- de Sitter space-time. 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 arXiv:1406.2663v2 [hep-th] 23 Jun 2014 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.
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