1313010.1007/13130.1029-8479Journal of High Energy PhysicsJ. High Energ. Phys.1029-8479Springer Berlin HeidelbergBerlin/HeidelbergJHEP10(2024)068246492407.0626010.1007/JHEP10(2024)068Regular Article - Theoretical PhysicsThe light we can see: extracting black holes from weak Jacobi formshttp://orcid.org/0000-0002-3072-3758ApoloLuis1http://orcid.org/0000-0003-4444-7624BintanjaSuzanne23http://orcid.org/0000-0003-1485-8393CastroAlejandra4chttp://orcid.org/0000-0001-5824-8250LiskaDiego2Beijing Institute of Mathematical Sciences and Applications101408BeijingChinahttps://ror.org/04dkp9463grid.7177.60000 0000 8499 2262Institute for Theoretical Physics and ∆-Institute for Theoretical PhysicsUniversity of AmsterdamPO Box 944851090GLAmsterdamThe Netherlandsgrid.133342.40000 0004 1936 9676Kavli Institute for Theoretical PhysicsUniversity of California93106Santa BarbaraCAUSAhttps://ror.org/013meh722grid.5335.00000 0001 2188 5934Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeCB3 0WACambridgeUnited Kingdomac2553@cam.ac.uk9102024102024202410689102024198202422920249102024© The Author(s) 20242024Open Access. 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.A<sc>bstract</sc>

We quantify how constraints on light states affect the asymptotic growth of heavy states in weak Jacobi forms. The constraints we consider are sparseness conditions on the Fourier coefficients of these forms, which are necessary to interpret them as gravitational path integrals. Using crossing kernels, we extract the leading and subleading behavior of these coefficients and show that the leading Cardy-like growth is robust in a wide regime of validity. On the other hand, we find that subleading corrections are sensitive to the constraints placed on the light states, and we quantify their imprint on the asymptotic growth of states. Our approach is tested against the generating function of symmetric product orbifolds, where we provide new insights into the factors contributing to the asymptotic growth of their Fourier coefficients. Finally, we use our methods to revisit the UV/IR connection that relates black hole microstate counting to modular forms. We provide a microscopic interpretation of the logarithmic corrections to the entropy of BPS black holes in N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = 2, 4 ungauged supergravity in four and five dimensions, and tie it to consistency conditions in AdS3/CFT2.

K<sc>eywords</sc>AdS-CFT CorrespondenceBlack Holes in String Theorypublisher-imprint-nameSpringervolume-issue-count12issue-article-count73issue-toc-levels0issue-pricelist-year2024issue-copyright-holderSISSA, Trieste, Italyissue-copyright-year2021article-contains-esmNoarticle-numbering-styleContentOnlyarticle-registration-date-year2024article-registration-date-month10article-registration-date-day9article-toc-levels0toc-levels0volume-typeRegularjournal-productArchiveJournalnumbering-styleUnnumberedarticle-grants-typeOpenChoicemetadata-grantOpenAccessabstract-grantOpenAccessbodypdf-grantOpenAccessbodyhtml-grantOpenAccessbibliography-grantOpenAccessesm-grantOpenAccessonline-firstfalsepdf-file-referenceBodyRef/PDF/13130_2024_Article_24649.pdfpdf-typeTypesettarget-typeOnlinePDFissue-typeRegulararticle-typeOriginalPaperjournal-subject-primaryPhysicsjournal-subject-secondaryElementary Particles, Quantum Field Theoryjournal-subject-secondaryQuantum Field Theories, String Theoryjournal-subject-secondaryClassical and Quantum Gravitation, Relativity Theoryjournal-subject-secondaryQuantum Physicsjournal-subject-collectionPhysics and Astronomyopen-accesstrue

ArXiv ePrint: 2407.06260

Acknowledgments

We thank Mert Besken, Alejandro Cabo-Bizet, Frederik Denef, Victor Godet, Gabriel Lopes-Cardoso, Sameer Murthy, Marti Rosello, Wei Song, and Fengjun Xu for helpful discussions. We also thank the participants and organizers of the Physics Sessions Initiative, Crete, 2023, and the participants of the Isaac Newton Institute for Mathematical Sciences programme “Black holes: bridges between number theory and holographic quantum information.” We also thank the organizers of the Amsterdam Summer String Workshop 2024 for their hospitality during the last stages of this work.

The work of LA was supported in part by the Dutch Research Council (NWO) through the Scanning New Horizons programme (16SNH02). The work of SB is supported by the Delta ITP consortium, a program of the Netherlands Organisation for Scientific Research (NWO) that is funded by the Dutch Ministry of Education, Culture and Science (OCW), and in part by the National Science Foundation under Grant No. NSF PHY-1748958, the Heising-Simons Foundation, and the Simons Foundation (216179, LB). DL is supported by the European Research Council under the European Unions Seventh Framework Programme (FP7/2007-2013), ERC Grant agreement ADG 834878. SB and AC would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme “Black holes: bridges between number theory and holographic quantum information” where work on this paper was undertaken. This work was supported by EPSRC grant no EP/R014604/1. This work has been partially supported by STFC consolidated grants ST/T000694/1 and ST/X000664/1. This research was supported in part by grant NSF PHY-2309135 to the Kavli Institute for Theoretical Physics (KITP).

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