Abstract
We initiate the study of holographic correlators for operators whose dimension scales with the central charge of the CFT. Differently from light correlators or probes, the insertion of any such maximally heavy operator changes the AdS metric, so that the correlator itself is dual to a backreacted geometry with marked points at the Poincaré boundary. We illustrate this new physics for two-point functions. Whereas the bulk description of light or probe operators involves Witten diagrams or extremal surfaces in an AdS background, the maximally heavy two-point functions are described by nontrivial new geometries which we refer to as “spacetime bananas”. As a universal example, we discuss the two-point function of maximally heavy scalar operators described by the Schwarzschild black hole in the bulk and we show that its onshell action reproduces the expected CFT result. This computation is nonstandard, and adding boundary terms to the action on the stretched horizon is crucial. Then, we verify the conformal Ward Identity from the holographic stress tensor and discuss important aspects of the Fefferman-Graham patch. Finally we study a Heavy-Heavy-Light-Light correlator by using geodesics propagating in the banana background. Our main motivation here is to set up the formalism to explore possible universal results for three- and higher-point functions of maximally heavy operators.
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Acknowledgments
We thank Stefano Baiguera, Scott Collier, Sergei Dubovsky, Tom Hartman, Davide Gaiotto, Luis Lehner, Raghu Mahajan, Juan Maldacena, Don Marolf, Leopoldo Pando-Zayas, Joao Penedones, Eric Perlmutter for useful comments and 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. Holography and correlation functions of huge operators: spacetime bananas. J. High Energ. Phys. 2023, 58 (2023). https://doi.org/10.1007/JHEP12(2023)058
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DOI: https://doi.org/10.1007/JHEP12(2023)058