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A Calabi-Yau database: threefolds constructed from the Kreuzer-Skarke list

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dc.contributor.authorAltman, Rossen
dc.contributor.authorGray, James A.en
dc.contributor.authorHe, Yang-Huien
dc.contributor.authorJejjala, Vishnuen
dc.contributor.authorNelson, Brent D.en
dc.contributor.departmentPhysicsen
dc.date.accessioned2019-03-11T15:27:13Zen
dc.date.available2019-03-11T15:27:13Zen
dc.date.issued2015-02-25en
dc.description.abstractKreuzer and Skarke famously produced the largest known database of Calabi-Yau threefolds by providing a complete construction of all 473,800,776 reflexive polyhedra that exist in four dimensions [1]. These polyhedra describe the singular limits of ambient toric varieties in which Calabi-Yau threefolds can exist as hypersurfaces. In this paper, we review how to extract topological and geometric information about Calabi-Yau threefolds using the toric construction, and we provide, in a companion online database (see http://nuweb1.neu.edu/cydatabase), a detailed inventory of these quantities which are of interest to physicists. Many of the singular ambient spaces described by the Kreuzer-Skarke list can be smoothed out into multiple distinct toric ambient spaces describing different Calabi-Yau threefolds. We provide a list of the different Calabi-Yau threefolds which can be obtained from each polytope, up to current computational limits. We then give the details of a variety of quantities associated to each of these Calabi-Yau such as Chern classes, intersection numbers, and the Kahler and Mori cones, in addition to the Hodge data. This data forms a useful starting point for a number of physical applications of the Kreuzer-Skarke list.en
dc.description.notesWe are grateful to Lara Anderson, Per Berglund, Volker Braun, Stefan Groot Nibbelink, Benjamin Jurke, Seung-Joo Lee, Andre Lukas, Herbie Smith, Xin Gao, and Chuang Sun for many helpful discussions during the development of this database. We especially thank Joan Simon for collaboration on a parallel work [63], which applies the database developed in this paper to classify Calabi-Yau threefolds admitting large volume vacua. Finally, we would also like to thank Balazs Szendroi for his valuable feedback on the topic of gluing Kahler cones. JG is supported by NSF PHY-1417316. YHH is supported by the Science and Technology Facilities Council, U.K., for grant ST/J00037X/1, the Chinese Ministry of Education, for a Chang-Jiang Chair Professorship at NanKai University, and the city of Tian-Jin for a Qian-Ren Award. VJ is supported by the South African Research Chairs Initiative of the Department of Science and Technology and National Research Foundation and thanks McGill University for hospitality. The work of the authors is funded by the U.S. National Science Foundation under the grant CCF-1048082, EAGER: CiC: a String Cartography.en
dc.description.sponsorshipNSF [PHY-1417316]en
dc.description.sponsorshipScience and Technology Facilities Council, U.K. [ST/J00037X/1]en
dc.description.sponsorshipChinese Ministry of Education, for a Chang-Jiang Chair Professorship at NanKai Universityen
dc.description.sponsorshipcity of Tian-Jin for a Qian-Ren Awarden
dc.description.sponsorshipSouth African Research Chairs Initiative of the Department of Science and Technologyen
dc.description.sponsorshipU.S. National Science Foundation [CCF-1048082]en
dc.description.sponsorshipNational Research Foundationen
dc.description.sponsorshipScience and Technology Facilities Council [ST/J00037X/1, ST/L000482/1]en
dc.format.mimetypeapplication/pdfen
dc.identifier.doihttps://doi.org/10.1007/JHEP02(2015)158en
dc.identifier.issn1029-8479en
dc.identifier.issue2en
dc.identifier.other158en
dc.identifier.urihttp://hdl.handle.net/10919/88411en
dc.language.isoen_USen
dc.publisherSpringeren
dc.rightsCreative Commons Attribution 4.0 Internationalen
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/en
dc.subjectDifferential and Algebraic Geometryen
dc.subjectSuperstring Vacuaen
dc.titleA Calabi-Yau database: threefolds constructed from the Kreuzer-Skarke listen
dc.title.serialJournal of High Energy Physicsen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten

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