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Published December 2020 | Submitted + Published
Journal Article Open

Building bulk geometry from the tensor Radon transform


Using the tensor Radon transform and related numerical methods, we study how bulk geometries can be explicitly reconstructed from boundary entanglement entropies in the specific case of AdS₃/CFT₂. We find that, given the boundary entanglement entropies of a 2d CFT, this framework provides a quantitative measure that detects whether the bulk dual is geometric in the perturbative (near AdS) limit. In the case where a well-defined bulk geometry exists, we explicitly reconstruct the unique bulk metric tensor once a gauge choice is made. We then examine the emergent bulk geometries for static and dynamical scenarios in holography and in many-body systems. Apart from the physics results, our work demonstrates that numerical methods are feasible and effective in the study of bulk reconstruction in AdS/CFT.

Additional Information

© 2020 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Received 09 September 2020; Accepted 29 October 2020; Published 04 December 2020. We thank Ping Gao, Vedran Lekic, Francois Monard, Chris Pattison, Gunther Uhlmann, Zhi-Cheng Yang, and Larry Zeng for helpful discussions. C.C., X.L.Q., and B.G.S. acknowledge the support by the DOE Office of Science, Office of High Energy Physics, through the grant de-sc0019380. C.C. is also supported by the U.S. Department of Defense and NIST through the Hartree Postdoctoral Fellowship at QuICS. C.C. and B.G.S. acknowledge the support by the Simons Foundation as part of the It From Qubit Collaboration. ET acknowledge funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NSF Grant PHY-1733907), the Simons Foundation It from Qubit Collaboration, the DOE QuantISED program (DE-SC0018407), and the Air Force Office of Scientific Research (FA9550-19-1-0360). ET also acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC).

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Published - Cao2020_Article_BuildingBulkGeometryFromTheTen.pdf

Submitted - 2007.00004.pdf


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