A Calabi-Yau Database: Threefolds Constructed from the Kreuzer-Skarke List

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. 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.

References in corpus (35)

• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
• An SU(5) Heterotic Standard Model
• A Heterotic Standard Model
• A Generalized Construction of Mirror Manifolds
• General Analysis of LARGE Volume Scenarios with String Loop Moduli Stabilisation
• Heterotic Line Bundle Standard Models
• The Exact MSSM Spectrum from String Theory
• PALP: A Package for Analyzing Lattice Polytopes with Applications to Toric Geometry
• Exploring Positive Monad Bundles And A New Heterotic Standard Model
• A Standard Model from the E8 x E8 Heterotic Superstring
• D-Branes at del Pezzo Singularities: Global Embedding and Moduli Stabilisation
• Explicit de Sitter Flux Vacua for Global String Models with Chiral Matter
• F-theory fluxes, Chirality and Chern-Simons theories
• Toric bases for 6D F-theory models
• All Complete Intersection Calabi-Yau Four-Folds
• Toric K3-Fibred Calabi-Yau Manifolds with del Pezzo Divisors for String Compactifications
• Topological Invariants and Fibration Structure of Complete Intersection Calabi-Yau Four-Folds
• New Higgs Transitions between Dual N=2 String Models
• On Classifying the Divisor Involutions in Calabi-Yau Threefolds
• Heterotic Models from Vector Bundles on Toric Calabi-Yau Manifolds
• Geometric constraints in dual F-theory and heterotic string compactifications
• Integral Cohomology and Mirror Symmetry for Calabi-Yau 3-folds
• Complete toric varieties with reductive automorphism group
• Heavy Tails in Calabi-Yau Moduli Spaces
• Mirror Symmetry and the Moduli Space for Generic Hypersurfaces in Toric Varieties
• A Note on Poly-Instanton Effects in Type IIB Orientifolds on Calabi-Yau Threefolds
• The MSSM Spectrum from (0,2)-Deformations of the Heterotic Standard Embedding
• PALP - a User Manual
• Toric Methods in F-theory Model Building
• F-term Stabilization of Odd Axions in LARGE Volume Scenario
• The Geometer's Toolkit to String Compactifications
• Unification of M- and F- Theory Calabi-Yau Fourfold Vacua
• Heterotic Model Building: 16 Special Manifolds
• Heterotic Bundles on Calabi-Yau Manifolds with Small Picard Number
• A new offspring of PALP

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• Global Embedding of Fibre Inflation Models
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• The Standard Model Quiver in de Sitter String Compactifications
• Chiral Global Embedding of Fibre Inflation Models
• On de Sitter String Vacua from Anti-D3-Branes in the Large Volume Scenario
• Getting CICY High
• Large Field Inflation from Axion Mixing
• LVS de Sitter Vacua are probably in the Swampland
• The Calabi-Yau Landscape: from Geometry, to Physics, to Machine-Learning
• Systematics of Axion Inflation in Calabi-Yau Hypersurfaces
• Estimating Calabi-Yau Hypersurface and Triangulation Counts with Equation Learners
• Topological Constraints in the LARGE-Volume Scenario
• On Calabi-Yau generalized complete intersections from Hirzebruch varieties and novel K3-fibrations
• On de Sitter Spacetime and String Theory
• Calabi-Yau Volumes and Reflexive Polytopes
• Orientifold Calabi-Yau Threefolds with Divisor Involutions and String Landscape
• De Sitter vacua from a D-term generated racetrack potential in hypersurface Calabi-Yau compactifications
• New Calabi-Yau Manifolds from Genetic Algorithms
• Stabilising all Kähler moduli in perturbative LVS
• Rigid limit for hypermultiplets and five-dimensional gauge theories
• Moduli stabilization in type IIB orientifolds at $h^{2,1}=50$
• Natural Inflation from Near Alignment in Heterotic String Theory
• Applying machine learning to the Calabi-Yau orientifolds with string vacua
• Discrete Symmetries of Calabi-Yau Hypersurfaces in Toric Four-Folds
• Tools for CICYs in F-theory
• Non-toric bases for elliptic Calabi-Yau threefolds and 6D F-theory vacua
• A remark on generalized complete intersections
• Systematics of perturbatively flat flux vacua
• On K3-fibred LARGE Volume Scenario with de Sitter vacua from anti-D3-branes
• New Large Volume Solutions
• Higher Derivative Corrections to String Inflation
• SU-bordism: structure results and geometric representatives
• Chiral global embedding of Fibre Inflation with $\overline{D3}$ uplift
• Classifying divisor topologies for string phenomenology
• Inflating in perturbative LVS: Global Embedding and Robustness
• Polytopes and Machine Learning
• Jumping Spectra and Vanishing Couplings in Heterotic Line Bundle Standard Models
• Mirror pairs of Calabi-Yau threefolds from mirror pairs of quasi-Fano threefolds
• Patterns in Calabi-Yau Distributions
• Global Embedding of Fibre Inflation in Perturbative LVS
• Kahler Moduli Inflation in Type IIB Compactifications: A random tumble through the Calabi-Yau landscape
• Aligned Natural Inflation in the Large Volume Scenario
• Universes as Big Data
• Chern-Simons Invariants and Heterotic Superpotentials
• Taming Triangulation Dependence of T6/Z2xZ2 Resolutions
• Futaki Invariants and Reflexive Polygons
• Quiver Gauge Theories: Beyond Reflexivity
• Calabi-Yau Four/Five/Six-folds as ${\mathbb{P}}_{\text{w}}^n$ Hypersurfaces: Machine Learning, Approximation, and Generation
• Line bundle embeddings for heterotic theories
• Early Universe Cosmology, Effective Supergravity, and Invariants of Algebraic Forms
• Assisted Fibre Inflation in Perturbative LVS
• Hybrid Inflation, Reheating and Dark Radiation in a IIB perturbative moduli stabilization scenario
• The Tadpole Conjecture in Asymptotic Limits
• An example of non-Kähler Calabi-Yau fourfold
• $d$-semistable Calabi--Yau threefolds of Type III
• Divisor topologies of CICY 3-folds and their applications to phenomenology
• Tracing symmetries and their breakdown through phases of heterotic (2,2) compactifications
• A Database of Calabi-Yau Orientifolds and the Size of D3-Tadpoles