Journal of High Energy Physics

, 2015:158 | Cite as

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

  • Ross Altman
  • James Gray
  • Yang-Hui He
  • Vishnu Jejjala
  • Brent D. Nelson
Open Access
Regular Article - Theoretical Physics

Abstract

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 Kähler 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.

Keywords

Differential and Algebraic Geometry Superstring Vacua 

Notes

Open 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.

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Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Ross Altman
    • 1
  • James Gray
    • 2
  • Yang-Hui He
    • 3
    • 4
    • 5
  • Vishnu Jejjala
    • 6
  • Brent D. Nelson
    • 1
    • 7
  1. 1.Department of PhysicsNortheastern UniversityBostonU.S.A.
  2. 2.Physics Department, Robeson Hall, Virginia TechBlacksburgU.S.A.
  3. 3.Department of MathematicsCity UniversityLondonU.K.
  4. 4.School of PhysicsNanKai UniversityTianjinP.R. China
  5. 5.Merton CollegeUniversity of OxfordOxfordU.K.
  6. 6.Centre for Theoretical Physics, NITheP, and School of PhysicsUniversity of the WitwatersrandJohannesburgSouth Africa
  7. 7.International Center for Theoretical PhysicsTriesteItaly

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