A Calabi-Yau database: threefolds constructed from the Kreuzer-Skarke list
| Autor: | James Gray, Vishnu Jejjala, Brent D. Nelson, Ross Altman, Yang-Hui He |
|---|---|
| Přispěvatelé: | Physics |
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Physics
High Energy Physics - Theory Nuclear and High Energy Physics Chern class Current (mathematics) Database Superstring Vacua FOS: Physical sciences Polytope computer.software_genre Polyhedron Mathematics - Algebraic Geometry Singularity Mathematics::Algebraic Geometry High Energy Physics - Theory (hep-th) Intersection FOS: Mathematics Calabi–Yau manifold Differential and Algebraic Geometry Mathematics::Differential Geometry Variety (universal algebra) QA Algebraic Geometry (math.AG) computer Mathematics::Symplectic Geometry |
| Zdroj: | Journal of High Energy Physics |
| Popis: | Kreuzer 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. NSF [PHY-1417316] Science and Technology Facilities Council, U.K. [ST/J00037X/1] Chinese Ministry of Education, for a Chang-Jiang Chair Professorship at NanKai University city of Tian-Jin for a Qian-Ren Award South African Research Chairs Initiative of the Department of Science and Technology U.S. National Science Foundation [CCF-1048082] National Research Foundation Science and Technology Facilities Council [ST/J00037X/1, ST/L000482/1] We 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. |
| Databáze: | OpenAIRE |
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