Abstract
We describe solutions of asymptotically AdS3 Einstein gravity that are sourced by the insertion of operators in the boundary CFT2, whose dimension scales with the central charge of the theory. Previously, we found that the geometry corresponding to a black hole two-point function is simply related to an infinite covering of the Euclidean BTZ black hole [1]. However, here we find that the geometry sourced by the presence of a third black hole operator turns out to be a Euclidean wormhole with two asymptotic boundaries. We construct this new geometry as a quotient of empty AdS3 realized by domes and doors. The doors give access to the infinite covers that are needed to describe the insertion of the operators, while the domes describe the fundamental domains of the quotient on each cover. In particular, despite the standard fact that the Fefferman-Graham expansion is single-sided, the extended bulk geometry contains a wormhole that connects two asymptotic boundaries. We observe that the two-sided wormhole can be made single-sided by cutting off the wormhole and gluing on a “Lorentzian cap”. In this way, the geometry gives the holographic description of a three-point function, up to phases. By rewriting the metric in terms of a Liouville field, we compute the on-shell action and find that the result matches with the Heavy-Heavy-Heavy three-point function predicted by the modular bootstrap. Finally, we describe the geometric transition between doors and defects, that is, when one or more dual operators describe a conical defect insertion, rather than a black hole insertion.
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Acknowledgments
We thank Nathan Benjamin, Nathan Berkovits, Scott Collier, Sergei Dubovsky, Tom Hartman, Davide Gaiotto, Juan Maldacena, Dalimil Mazac, Joao Penedones, Eric Perlmutter and David Simon-Duffins, for useful comments and discussions. JA also thanks Suzanne Bintanja, Jeevan Chandra and Gabriele Di Ubaldo for discussions. FA also thanks Kostas Skenderis, Marika Taylor and David Turton for discussions. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science, and Economic Development Canada and by the Province of Ontario through the Ministry of Colleges and Universities. RCM and PV are supported in part by Discovery Grants from the Natural Sciences and Engineering Research Council of Canada, and by the Simons Foundation through the “It from Qubit” and the “Nonperturbative Bootstrap” collaborations, respectively (PV: #488661). This work was additionally supported by FAPESP Foundation through the grants 2016/01343-7, 2017/03303-1, 2020/16337-8. JA, FA and PV thank the organizers of the conference “Gravity from Algebra: Modern Field Theory Methods for Holography”, and acknowledge KITP for hospitality. Research at KITP is supported in part by the National Science Foundation under Grant No. NSF PHY-1748958. FA is supported by the Ramon y Cajal program through the fellowship RYC2021-031627-I funded by MCIN/AEI/10.13039/501100011033 and by the European Union NextGenerationEU/PRTR.
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Abajian, J., Aprile, F., Myers, R.C. et al. Correlation functions of huge operators in AdS3/CFT2: domes, doors and book pages. J. High Energ. Phys. 2024, 118 (2024). https://doi.org/10.1007/JHEP03(2024)118
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DOI: https://doi.org/10.1007/JHEP03(2024)118