On the prevalence of elliptic and genus one fibrations among toric hypersurface Calabi-Yau threefolds

Huang, Yu-Chien; Taylor, Washington

doi:10.1007/jhep03(2019)014

Title: On the prevalence of elliptic and genus one fibrations among toric hypersurface Calabi-Yau threefolds

Abstract

We systematically analyze the fibration structure of toric hypersurface Calabi-Yau threefolds with large and small Hodge numbers. We show that there are only four such Calabi-Yau threefolds with h1,1 ≥ 140 or h2,1 ≥ 140 that do not have manifest elliptic or genus one fibers arising from a fibration of the associated 4D polytope. There is a genus one fibration whenever either Hodge number is 150 or greater, and an elliptic fibration when either Hodge number is 228 or greater. We find that for small h1,1 the fraction of polytopes in the KS database that do not have a genus one or elliptic fibration drops exponentially as h1,1 increases. We also consider the different toric fiber types that arise in the polytopes of elliptic Calabi-Yau threefolds.

Authors:

Huang, Yu-Chien ^[1]; Taylor, Washington ^[1]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Publication Date:: Tue Mar 05 00:00:00 EST 2019

Research Org.:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:: 1611866

Grant/Contract Number:: SC0012567

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2019; Journal Issue: 3; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics; Differential and Algebraic Geometry; F-Theory

Citation Formats


                    Huang, Yu-Chien, and Taylor, Washington. On the prevalence of elliptic and genus one fibrations among toric hypersurface Calabi-Yau threefolds.  United States: N. p., 2019. 
Web.  doi:10.1007/jhep03(2019)014.

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                    Huang, Yu-Chien, & Taylor, Washington. On the prevalence of elliptic and genus one fibrations among toric hypersurface Calabi-Yau threefolds.  United States.  https://doi.org/10.1007/jhep03(2019)014

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                    Huang, Yu-Chien, and Taylor, Washington. Tue .  
"On the prevalence of elliptic and genus one fibrations among toric hypersurface Calabi-Yau threefolds".  United States.  https://doi.org/10.1007/jhep03(2019)014.  https://www.osti.gov/servlets/purl/1611866.

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@article{osti_1611866,

  title        = {On the prevalence of elliptic and genus one fibrations among toric hypersurface Calabi-Yau threefolds},

  author       = {Huang, Yu-Chien and Taylor, Washington},

  abstractNote = {We systematically analyze the fibration structure of toric hypersurface Calabi-Yau threefolds with large and small Hodge numbers. We show that there are only four such Calabi-Yau threefolds with h1,1 ≥ 140 or h2,1 ≥ 140 that do not have manifest elliptic or genus one fibers arising from a fibration of the associated 4D polytope. There is a genus one fibration whenever either Hodge number is 150 or greater, and an elliptic fibration when either Hodge number is 228 or greater. We find that for small h1,1 the fraction of polytopes in the KS database that do not have a genus one or elliptic fibration drops exponentially as h1,1 increases. We also consider the different toric fiber types that arise in the polytopes of elliptic Calabi-Yau threefolds.},

  doi          = {10.1007/jhep03(2019)014},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 3,

  volume       = 2019,

  place        = {United States},

  year         = {Tue Mar 05 00:00:00 EST 2019},

  month        = {Tue Mar 05 00:00:00 EST 2019}

}

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Works referenced in this record:

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Works referencing / citing this record:

Phases of 5d SCFTs from M-/F-theory on non-flat fibrations
journal, May 2019

Apruzzi, Fabio; Lin, Ling; Mayrhofer, Christoph
Journal of High Energy Physics, Vol. 2019, Issue 5
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Modularity from monodromy
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Topological strings on genus one fibered Calabi-Yau 3-folds and string dualities
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Cota, Cesar Fierro; Klemm, Albrecht; Schimannek, Thorsten
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Modularity from Monodromy
text, January 2019

Schimannek, Thorsten
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Title: On the prevalence of elliptic and genus one fibrations among toric hypersurface Calabi-Yau threefolds

Abstract

Citation Formats

On the Hodge structure of elliptically fibered Calabi-Yau threefolds journal, August 2012

Cubic Forms in Ten Variables journal, September 1983

String dualities and toric geometry: an introduction journal, February 1999

TASI Lectures on Abelian and Discrete Symmetries in F-theory conference, September 2018

Topological invariants and fibration structure of complete intersection Calabi-Yau four-folds journal, September 2014

Fibrations in CICY threefolds journal, October 2017

Calabi-Yau 4-folds and toric fibrations journal, July 1998

hypersurfaces in algebraic tori journal, February 1993

A finiteness theorem for elliptic Calabi-Yau threefolds journal, May 1994

Tools for CICYs in F-theory journal, November 2016

Arithmetic on elliptic threefolds journal, May 2004

Complete classification of reflexive polyhedra in four dimensions journal, January 2000

Toric elliptic fibrations and F-theory compactifications journal, January 2013

F-theory on all toric hypersurface fibrations and its Higgs branches journal, January 2015

The existence of elliptic fibre space structures on Calabi-Yau threefolds journal, September 1994

All complete intersection Calabi-Yau four-folds journal, July 2013

A new construction of Calabi–Yau manifolds: Generalized CICYs journal, May 2016

F-theory on genus-one fibrations journal, August 2014

Fibrations in non-simply connected Calabi-Yau quotients journal, August 2018

Mordell-Weil torsion and the global structure of gauge groups in F-theory journal, October 2014

Multiple fibrations in Calabi-Yau geometry and string dualities journal, October 2016

Affine Kac-Moody algebras, CHL strings and the classification of tops journal, January 2003

A Remark on Indeterminate Equations in Several Variables journal, April 1937

On minimal models of elliptic threefolds journal, March 1991

Evidence for F-theory journal, June 1996

Comparing elliptic and toric hypersurface Calabi-Yau threefolds at large Hodge numbers journal, February 2019

Vacuum configurations for superstrings journal, January 1985

Compactifications of F-theory on Calabi-Yau threefolds. (I) journal, August 1996

Compactifications of F-theory on Calabi-Yau threefolds (II) journal, September 1996

Physics of F-theory compactifications without section journal, December 2014

F-theory vacua with Z 3 gauge symmetry journal, September 2015

Global aspects of the space of 6D $ \mathcal{N} = 1 $ supergravities journal, November 2010

An Abundance of K3 Fibrations from Polyhedra with Interchangeable Parts journal, October 2013

Classifying bases for 6D F-theory models journal, January 2012

Toric bases for 6D F-theory models journal, May 2012

Non-toric bases for elliptic Calabi–Yau threefolds and 6D F-theory vacua journal, January 2017

Calabi-Yau threefolds with large h 2,1 journal, October 2014

Enhanced gauge symmetry in 6D F-theory models and tuned elliptic Calabi-Yau threefolds: Enhanced gauge symmetry in 6D F-theory models… journal, August 2016

Duality between the webs of heterotic and type II vacua journal, February 1998

Geometric engineering in toric F-theory and GUTs with U(1) gauge factors journal, December 2013

Scanning the skeleton of the 4D F-theory landscape journal, January 2018

On Algebraic Fiber Space Structures on a Calabi-Yau 3-Fold journal, June 1993

Algorithmic universality in F-theory compactifications journal, December 2017

A new construction of Calabi–Yau manifolds: Generalized CICYs other, January 2016

F-Theory on all Toric Hypersurface Fibrations and its Higgs Branches text, January 2014

F-Theory Vacua with Z_3 Gauge Symmetry text, January 2015

Calabi-Yau 4-folds and toric fibrations text, January 1997

String Dualities and Toric Geometry: An Introduction text, January 1998

Phases of 5d SCFTs from M-/F-theory on non-flat fibrations journal, May 2019

Modularity from monodromy journal, May 2019

Topological strings on genus one fibered Calabi-Yau 3-folds and string dualities journal, November 2019

Phases of 5d SCFTs from M-/F-theory on Non-Flat Fibrations text, January 2018

Modularity from Monodromy text, January 2019

On the Hodge structure of elliptically fibered Calabi-Yau threefolds
journal, August 2012

Cubic Forms in Ten Variables
journal, September 1983

String dualities and toric geometry: an introduction
journal, February 1999

TASI Lectures on Abelian and Discrete Symmetries in F-theory
conference, September 2018

Topological invariants and fibration structure of complete intersection Calabi-Yau four-folds
journal, September 2014

Fibrations in CICY threefolds
journal, October 2017

Calabi-Yau 4-folds and toric fibrations
journal, July 1998

hypersurfaces in algebraic tori
journal, February 1993

A finiteness theorem for elliptic Calabi-Yau threefolds
journal, May 1994

Tools for CICYs in F-theory
journal, November 2016

Arithmetic on elliptic threefolds
journal, May 2004

Complete classification of reflexive polyhedra in four dimensions
journal, January 2000

Toric elliptic fibrations and F-theory compactifications
journal, January 2013

F-theory on all toric hypersurface fibrations and its Higgs branches
journal, January 2015

The existence of elliptic fibre space structures on Calabi-Yau threefolds
journal, September 1994

All complete intersection Calabi-Yau four-folds
journal, July 2013

A new construction of Calabi–Yau manifolds: Generalized CICYs
journal, May 2016

F-theory on genus-one fibrations
journal, August 2014

Fibrations in non-simply connected Calabi-Yau quotients
journal, August 2018

Mordell-Weil torsion and the global structure of gauge groups in F-theory
journal, October 2014

Multiple fibrations in Calabi-Yau geometry and string dualities
journal, October 2016

Affine Kac-Moody algebras, CHL strings and the classification of tops
journal, January 2003

A Remark on Indeterminate Equations in Several Variables
journal, April 1937

On minimal models of elliptic threefolds
journal, March 1991

Evidence for F-theory
journal, June 1996

Comparing elliptic and toric hypersurface Calabi-Yau threefolds at large Hodge numbers
journal, February 2019

Vacuum configurations for superstrings
journal, January 1985

Compactifications of F-theory on Calabi-Yau threefolds. (I)
journal, August 1996

Compactifications of F-theory on Calabi-Yau threefolds (II)
journal, September 1996

Physics of F-theory compactifications without section
journal, December 2014

F-theory vacua with $Z_{3}$ gauge symmetry
journal, September 2015

Global aspects of the space of 6D $ \mathcal{N} = 1 $ supergravities
journal, November 2010

An Abundance of K3 Fibrations from Polyhedra with Interchangeable Parts
journal, October 2013

Classifying bases for 6D F-theory models
journal, January 2012

Toric bases for 6D F-theory models
journal, May 2012

Non-toric bases for elliptic Calabi–Yau threefolds and 6D F-theory vacua
journal, January 2017

Calabi-Yau threefolds with large h 2,1
journal, October 2014

Enhanced gauge symmetry in 6D F-theory models and tuned elliptic Calabi-Yau threefolds: Enhanced gauge symmetry in 6D F-theory models…
journal, August 2016

Duality between the webs of heterotic and type II vacua
journal, February 1998

Geometric engineering in toric F-theory and GUTs with U(1) gauge factors
journal, December 2013

Scanning the skeleton of the 4D F-theory landscape
journal, January 2018

On Algebraic Fiber Space Structures on a Calabi-Yau 3-Fold
journal, June 1993

Algorithmic universality in F-theory compactifications
journal, December 2017

A new construction of Calabi–Yau manifolds: Generalized CICYs
other, January 2016

F-Theory on all Toric Hypersurface Fibrations and its Higgs Branches
text, January 2014

F-Theory Vacua with Z_3 Gauge Symmetry
text, January 2015

Calabi-Yau 4-folds and toric fibrations
text, January 1997

String Dualities and Toric Geometry: An Introduction
text, January 1998

Phases of 5d SCFTs from M-/F-theory on non-flat fibrations
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Modularity from monodromy
journal, May 2019

Topological strings on genus one fibered Calabi-Yau 3-folds and string dualities
journal, November 2019

Phases of 5d SCFTs from M-/F-theory on Non-Flat Fibrations
text, January 2018

Modularity from Monodromy
text, January 2019