The Gromov-Witten instanton expansion of the 4D N=2 prepotential is reinterpreted as a spectral decomposition into eigenfunctions of a Laplace-Beltrami operator on the Coxeter quotient of the moduli space, explaining the natural appearance of Bessel and theta functions for dihedral groups.
Fibrations in CICY Threefolds
8 Pith papers cite this work. Polarity classification is still indexing.
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abstract
In this work we systematically enumerate genus one fibrations in the class of 7,890 Calabi-Yau manifolds defined as complete intersections in products of projective spaces, the so-called CICY threefolds. This survey is independent of the description of the manifolds and improves upon past approaches that probed only a particular algebraic form of the threefolds (i.e. searches for "obvious" genus one fibrations as in [1,2]). We also study K3-fibrations and nested fibration structures. That is, K3 fibrations with potentially many distinct elliptic fibrations. To accomplish this survey a number of new geometric tools are developed including a determination of the full topology of all CICY threefolds, including triple intersection numbers. In 2,946 cases this involves finding a new "favorable" description of the manifold in which all divisors descend from a simple ambient space. Our results consist of a survey of obvious fibrations for all CICY threefolds and a complete classification of all genus one fibrations for 4,957 "Kahler favorable" CICYs whose Kahler cones descend from a simple ambient space. Within the CICY dataset, we find 139,597 obvious genus one fibrations, 30,974 obvious K3 fibrations and 208,987 nested combinations. For the Kahler favorable geometries we find a complete classification of 377,559 genus one fibrations. For one manifold with Hodge numbers (19,19) we find an explicit description of an infinite number of distinct genus-one fibrations extending previous results for this particular geometry that have appeared in the literature. The data associated to this scan is available at http://www1.phys.vt.edu/cicydata .
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A database scan identifies 2+14+45 Calabi-Yau threefolds with specified fibration and divisor structures that unify three LVS Kähler moduli inflation models.
Non-fibered Calabi-Yau threefolds in toric hypersurface and CICY classes connect to fibered Calabi-Yau threefolds via single-divisor shrinking transitions.
A Transformer trained by reinforcement learning generates heterotic line-bundle sums that satisfy anomaly-cancellation, stability, and chirality constraints, and its policy transfers usefully across Calabi-Yau geometries.
CIPro provides computational tools for complete intersection varieties and line bundles, including consolidated Calabi-Yau data for string theory applications.
A perturbative stabilization mechanism in the Large Volume Scenario for K3-fibered Calabi-Yau threefolds generates exponentially large 2D base volumes while keeping the 4D fibre small, enabling ADD or Dark Dimension limits with possible dS or quintessence vacua.
Coxeter symmetries from isomorphic flops in Kähler-favorable CICYs make the 4D N=2 prepotential solve the Helmholtz equation on the moduli space, enabling resummed expressions from worldsheet instantons.
Numerical Ricci-flat Calabi–Yau metrics turn string compactifications from topological existence statements into computable geometries, unlocking normalized couplings, spectra, and metric-level tests of mirror symmetry.
citing papers explorer
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Harmonic Analysis of the Instanton Prepotential
The Gromov-Witten instanton expansion of the 4D N=2 prepotential is reinterpreted as a spectral decomposition into eigenfunctions of a Laplace-Beltrami operator on the Coxeter quotient of the moduli space, explaining the natural appearance of Bessel and theta functions for dihedral groups.
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On Calabi-Yau Threefolds For Unified LVS Inflation
A database scan identifies 2+14+45 Calabi-Yau threefolds with specified fibration and divisor structures that unify three LVS Kähler moduli inflation models.
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An elliptic approach to Reid's fantasy
Non-fibered Calabi-Yau threefolds in toric hypersurface and CICY classes connect to fibered Calabi-Yau threefolds via single-divisor shrinking transitions.
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Exploring Line Bundle Standard Models with Transformers
A Transformer trained by reinforcement learning generates heterotic line-bundle sums that satisfy anomaly-cancellation, stability, and chirality constraints, and its policy transfers usefully across Calabi-Yau geometries.
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CIPro Package: Complete Intersections in Products of Projective Spaces and Line Bundles
CIPro provides computational tools for complete intersection varieties and line bundles, including consolidated Calabi-Yau data for string theory applications.
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Moduli Stabilisation for ADD and the Dark Dimension Scenario
A perturbative stabilization mechanism in the Large Volume Scenario for K3-fibered Calabi-Yau threefolds generates exponentially large 2D base volumes while keeping the 4D fibre small, enabling ADD or Dark Dimension limits with possible dS or quintessence vacua.
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Kaleidoscopes, Waves and the Prepotential
Coxeter symmetries from isomorphic flops in Kähler-favorable CICYs make the 4D N=2 prepotential solve the Helmholtz equation on the moduli space, enabling resummed expressions from worldsheet instantons.
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What to do with a Ricci-flat Calabi--Yau metric?
Numerical Ricci-flat Calabi–Yau metrics turn string compactifications from topological existence statements into computable geometries, unlocking normalized couplings, spectra, and metric-level tests of mirror symmetry.