Fibration structure in toric hypersurface Calabi-Yau threefolds

Huang, Yu-Chien; Taylor, Washington

doi:10.1007/jhep03(2020)172

Cited by 10 publications

(12 citation statements)

References 83 publications

(139 reference statements)

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“…A hint for what is going on is obtained from previous investigations into the underlying fibration structure of toric CY threefolds at large h 1,2 , see [49][50][51][52] and references therein. It is in fact true that CY threefolds in the KS database at sufficiently large Hodge numbers (h 1,2 larger than 240) are associated with elliptic fibrations over complex base surfaces [49].…”

Section: Large D3-charge and Genus-one Fibrationsmentioning

confidence: 97%

A Database of Calabi-Yau Orientifolds and the Size of D3-Tadpoles

Crinò,

Quevedo,

Schachner

et al. 2022

Preprint

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The classification of 4D reflexive polytopes by Kreuzer and Skarke allows for a systematic construction of Calabi-Yau hypersurfaces as fine, regular, star triangulations (FRSTs). Until now, the vastness of this geometric landscape remains largely unexplored. In this paper, we construct Calabi-Yau orientifolds from holomorphic reflection involutions of such hypersurfaces with Hodge numbers h 1,1 ≤ 12. In particular, we compute orientifold configurations for all favourable FRSTs for h 1,1 ≤ 7, while randomly sampling triangulations for each pair of Hodge numbers up to h 1,1 = 12. We find explicit string compactifications on these orientifolded Calabi-Yaus for which the D3-charge contribution coming from Op-planes grows linearly with the number of complex structure and Kähler moduli. We further consider nonlocal D7-tadpole cancellation through Whitney branes. We argue that this leads to a significant enhancement of the total D3-tadpole as compared to conventional SO(8) stacks with (4 + 4) D7-branes on top of O7-planes. In particular, before turningon worldvolume fluxes, we find that the largest D3-tadpole in this class occurs for Calabi-Yau threefolds with (h 1,1 + , h 1,2 − ) = (11, 491) with D3-brane charges |Q D3 | = 504 for the local D7 case and |Q D3 | = 6, 664 for the non-local Whitney branes case, which appears to be large enough to cancel tadpoles and allow fluxes to stabilise all complex structure moduli. Our data is publicly available under the following link https://github.com/AndreasSchachner/CY_Orientifold_database.

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Section: Large D3-charge and Genus-one Fibrationsmentioning

confidence: 97%

A Database of Calabi-Yau Orientifolds and the Size of D3-Tadpoles

Crinò,

Quevedo,

Schachner

et al. 2022

Preprint

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“…Recent work has highlighted the fact that the vast majority of known Calabi-Yau threefolds exhibit genus one fibrations [61,[72][73][74][75][76][77][78][79][80]. That is, they can be written as a fibration (i.e.…”

Section: Vanishing Tri-linear Couplings On Elliptically Fibered Manifoldsmentioning

confidence: 99%

“…Almost all known Calabi-Yau threefolds are elliptically fibered, and indeed often fibered in 10s or even hundreds of different ways (see e.g. [74,80]). Each of these different fibrations will contribute its own vanishing conditions.…”

Section: Jhep05(2021)085mentioning

confidence: 99%

Generalized vanishing theorems for Yukawa couplings in heterotic compactifications

Anderson

Gray

Larfors

et al. 2021

J. High Energ. Phys.

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Heterotic compactifications on Calabi-Yau threefolds frequently exhibit textures of vanishing Yukawa couplings in their low energy description. The vanishing of these couplings is often not enforced by any obvious symmetry and appears to be topological in nature. Recent results used differential geometric methods to explain the origin of some of this structure [1, 2]. A vanishing theorem was given which showed that the effect could be attributed, in part, to the embedding of the Calabi-Yau manifolds of interest inside higher dimensional ambient spaces, if the gauge bundles involved descended from vector bundles on those larger manifolds. In this paper, we utilize an algebro-geometric approach to provide an alternative derivation of some of these results, and are thus able to generalize them to a much wider arena than has been considered before. For example, we consider cases where the vector bundles of interest do not descend from bundles on the ambient space. In such a manner we are able to highlight the ubiquity with which textures of vanishing Yukawa couplings can be expected to arise in heterotic compactifications, with multiple different constraints arising from a plethora of different geometric features associated to the gauge bundle.

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“…In this work, we will focus on Calabi-Yau threefolds with an elliptic fibration 1 [23][24][25][26][27][28][29][30], and study how its complex structure moduli can be stabilized by bundle holomorphy. Bundles on an elliptically fibered Calabi-Yau threefold can be constructed by spectral data [31][32][33][34], which can be mapped to the extension or monad bundles by a Fourier-Mukai transformation.…”

Section: Introductionmentioning

confidence: 99%

Heterotic complex structure moduli stabilization for elliptically fibered Calabi-Yau manifolds

Cui

Karkheiran

2021

J. High Energ. Phys.

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Holomorphicity of vector bundles can stabilize complex structure moduli of a Calabi-Yau threefold in N = 1 supersymmetric heterotic compactifications. In principle, the Atiyah class determines the stabilized moduli. In this paper, we study how this mechanism works in the context of elliptically fibered Calabi-Yau manifolds where the complex structure moduli space contains two kinds of moduli, those from the base and those from the fibration. Defining the bundle with spectral data, we find three types of situations when bundles’ holomorphicity depends on algebraic cycles exist only for special loci in the complex structure moduli, which allows us to stabilize both of these two moduli. We present concrete examples for each type and develop practical tools to analyze the stabilized moduli. Finally, by checking the holomorphicity of the four-flux and/or local Higgs bundle data in F-theory, we briefly study the dual complex structure moduli stabilization scenarios.

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Fibration structure in toric hypersurface Calabi-Yau threefolds

Cited by 10 publications

References 83 publications

A Database of Calabi-Yau Orientifolds and the Size of D3-Tadpoles

A Database of Calabi-Yau Orientifolds and the Size of D3-Tadpoles

Generalized vanishing theorems for Yukawa couplings in heterotic compactifications

Heterotic complex structure moduli stabilization for elliptically fibered Calabi-Yau manifolds

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