1313010.1007/13130.1029-8479Journal of High Energy PhysicsJ. High Energ. Phys.1029-8479Springer Berlin HeidelbergBerlin/HeidelbergJHEP12(2023)025223352304.0686510.1007/JHEP12(2023)025Regular Article - Theoretical PhysicsCosmological quantum states of de Sitter-Schwarzschild are static patch partition functionsBlackerMatthew J.1HartnollSean A.1bhttps://ror.org/013meh722grid.5335.00000 0001 2188 5934Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeCB3 0WACambridgeUKs.a.hartnoll@damtp.cam.ac.uk4122023122023202312254122023246202314112023251120234122023© The Author(s) 20232023Open 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 solve the Wheeler-DeWitt equation in the ‘cosmological interior’ (the past causal diamond of future infinity) of four dimensional dS-Schwarzschild spacetimes. Within minisuperspace there is a basis of solutions labelled by a constant c, conjugate to the mass of the black hole. We propose that these solutions are in correspondence with partition functions of a dual quantum mechanical theory where c plays the role of time. The quantum mechanical theory lives on worldtubes in the ‘static patch’ of dS-Schwarzschild, and the partition function is obtained by evolving the corresponding Wheeler-DeWitt wavefunction through the cosmological horizon, where a metric component gtt changes sign. We establish that the dual theory admits a symmetry algebra given by a central extension of the Poincaré algebra e\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathfrak{e} $$\end{document}(1, 1) and that the entropy of the dS black hole is encoded as an averaging of the dual partition function over the background gtt.

K<sc>eywords</sc>de Sitter spaceAdS-CFT CorrespondenceBlack Holespublisher-imprint-nameSpringervolume-issue-count12issue-article-count23issue-toc-levels0issue-pricelist-year2023issue-copyright-holderSISSA, Trieste, Italyissue-copyright-year2021article-contains-esmNoarticle-numbering-styleContentOnlyarticle-registration-date-year2023article-registration-date-month12article-registration-date-day4article-toc-levels0toc-levels0volume-typeRegularjournal-productArchiveJournalnumbering-styleUnnumberedarticle-grants-typeOpenChoicemetadata-grantOpenAccessabstract-grantOpenAccessbodypdf-grantOpenAccessbodyhtml-grantOpenAccessbibliography-grantOpenAccessesm-grantOpenAccessonline-firstfalsepdf-file-referenceBodyRef/PDF/13130_2023_Article_22335.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: 2304.06865

Acknowledgments

It is a pleasure to acknowledge inspiring discussions with Dionysios Anninos, Diego Hofman, Albert Law and Ronak Soni. The work of S.A.H. is partially supported by Simons Investigator award #620869 and by STFC consolidated grant ST/T000694/1. M.J.B. was supported by a Gates Cambridge Scholarship (#OPP1144).

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