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

Journal Article · Tue Mar 05 00:00:00 EST 2019 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep03(2019)014· OSTI ID:1611866

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

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

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.

View Accepted Manuscript (DOE)

Cite

Export

Save

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

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

Grant/Contract Number:: SC0012567

OSTI ID:: 1611866

Journal Information:: Journal of High Energy Physics (Online), Vol. 2019, Issue 3; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 19 works

Citation information provided by
Web of Science

References (48)

On the Hodge structure of elliptically fibered Calabi-Yau threefolds Taylor, Washington Journal of High Energy Physics, Vol. 2012, Issue 8 https://doi.org/10.1007/JHEP08(2012)032	journal	August 2012
Cubic Forms in Ten Variables Heath-Brown, D. R. Proceedings of the London Mathematical Society, Vol. s3-47, Issue 2 https://doi.org/10.1112/plms/s3-47.2.225	journal	September 1983
String dualities and toric geometry: an introduction Skarke, H. Chaos, Solitons & Fractals, Vol. 10, Issue 2-3 https://doi.org/10.1016/S0960-0779(98)00161-1	journal	February 1999
TASI Lectures on Abelian and Discrete Symmetries in F-theory Cvetic, Mirjam; Lin, Ling Proceedings of Theoretical Advanced Study Institute Summer School 2017 "Physics at the Fundamental Frontier" — PoS(TASI2017) https://doi.org/10.22323/1.305.0020	conference	September 2018
Topological invariants and fibration structure of complete intersection Calabi-Yau four-folds Gray, James; Haupt, Alexander S.; Lukas, Andre Journal of High Energy Physics, Vol. 2014, Issue 9 https://doi.org/10.1007/JHEP09(2014)093	journal	September 2014
Fibrations in CICY threefolds Anderson, Lara B.; Gao, Xin; Gray, James Journal of High Energy Physics, Vol. 2017, Issue 10 https://doi.org/10.1007/JHEP10(2017)077	journal	October 2017
Calabi-Yau 4-folds and toric fibrations Kreuzer, Maximilian; Skarke, Harald Journal of Geometry and Physics, Vol. 26, Issue 3-4 https://doi.org/10.1016/S0393-0440(97)00059-4	journal	July 1998
hypersurfaces in algebraic tori Batyrev, Victor V. Duke Mathematical Journal, Vol. 69, Issue 2 https://doi.org/10.1215/S0012-7094-93-06917-7	journal	February 1993
A finiteness theorem for elliptic Calabi-Yau threefolds Gross, Mark Duke Mathematical Journal, Vol. 74, Issue 2 https://doi.org/10.1215/S0012-7094-94-07414-0	journal	May 1994
Tools for CICYs in F-theory Anderson, Lara B.; Gao, Xin; Gray, James Journal of High Energy Physics, Vol. 2016, Issue 11 https://doi.org/10.1007/JHEP11(2016)004	journal	November 2016
Arithmetic on elliptic threefolds Wazir, Rania Compositio Mathematica, Vol. 140, Issue 03 https://doi.org/10.1112/S0010437X03000381	journal	May 2004
Complete classification of reflexive polyhedra in four dimensions Kreuzer, Maximilian; Skarke, Harald Advances in Theoretical and Mathematical Physics, Vol. 4, Issue 6 https://doi.org/10.4310/ATMP.2000.v4.n6.a2	journal	January 2000
Toric elliptic fibrations and F-theory compactifications Braun, Volker Journal of High Energy Physics, Vol. 2013, Issue 1 https://doi.org/10.1007/JHEP01(2013)016	journal	January 2013
F-theory on all toric hypersurface fibrations and its Higgs branches Klevers, Denis; Mayorga Peña, Damián Kaloni; Oehlmann, Paul-Konstantin Journal of High Energy Physics, Vol. 2015, Issue 1 https://doi.org/10.1007/JHEP01(2015)142	journal	January 2015
The existence of elliptic fibre space structures on Calabi-Yau threefolds Wilson, P. M. H. Mathematische Annalen, Vol. 300, Issue 1 https://doi.org/10.1007/BF01450510	journal	September 1994
All complete intersection Calabi-Yau four-folds Gray, James; Haupt, Alexander S.; Lukas, Andre Journal of High Energy Physics, Vol. 2013, Issue 7 https://doi.org/10.1007/JHEP07(2013)070	journal	July 2013
A new construction of Calabi–Yau manifolds: Generalized CICYs Anderson, Lara B.; Apruzzi, Fabio; Gao, Xin Nuclear Physics B, Vol. 906 https://doi.org/10.1016/j.nuclphysb.2016.03.016	journal	May 2016
F-theory on genus-one fibrations Braun, Volker; Morrison, David R. Journal of High Energy Physics, Vol. 2014, Issue 8 https://doi.org/10.1007/JHEP08(2014)132	journal	August 2014
Fibrations in non-simply connected Calabi-Yau quotients Anderson, Lara B.; Gray, James; Hammack, Brian Journal of High Energy Physics, Vol. 2018, Issue 8 https://doi.org/10.1007/JHEP08(2018)128	journal	August 2018
Mordell-Weil torsion and the global structure of gauge groups in F-theory Mayrhofer, Christoph; Morrison, David R.; Till, Oskar Journal of High Energy Physics, Vol. 2014, Issue 10 https://doi.org/10.1007/JHEP10(2014)016	journal	October 2014
Multiple fibrations in Calabi-Yau geometry and string dualities Anderson, Lara B.; Gao, Xin; Gray, James Journal of High Energy Physics, Vol. 2016, Issue 10 https://doi.org/10.1007/JHEP10(2016)105	journal	October 2016
Affine Kac-Moody algebras, CHL strings and the classification of tops Bouchard, Vincent; Skarke, Harald Advances in Theoretical and Mathematical Physics, Vol. 7, Issue 2 https://doi.org/10.4310/ATMP.2003.v7.n2.a1	journal	January 2003
A Remark on Indeterminate Equations in Several Variables Mordell, L. J. Journal of the London Mathematical Society, Vol. s1-12, Issue 2 https://doi.org/10.1112/jlms/s1-12.1.127	journal	April 1937
On minimal models of elliptic threefolds Grassi, Antonella Mathematische Annalen, Vol. 290, Issue 1 https://doi.org/10.1007/BF01459246	journal	March 1991
Evidence for F-theory Vafa, Cumrun Nuclear Physics B, Vol. 469, Issue 3 https://doi.org/10.1016/0550-3213(96)00172-1	journal	June 1996
Comparing elliptic and toric hypersurface Calabi-Yau threefolds at large Hodge numbers Huang, Yu-Chien; Taylor, Washington Journal of High Energy Physics, Vol. 2019, Issue 2 https://doi.org/10.1007/JHEP02(2019)087	journal	February 2019
Vacuum configurations for superstrings Candelas, P.; Horowitz, Gary T.; Strominger, Andrew Nuclear Physics B, Vol. 258 https://doi.org/10.1016/0550-3213(85)90602-9	journal	January 1985
Compactifications of F-theory on Calabi-Yau threefolds. (I) Morrison, David R.; Vafa, Cumrun Nuclear Physics B, Vol. 473, Issue 1-2 https://doi.org/10.1016/0550-3213(96)00242-8	journal	August 1996
Compactifications of F-theory on Calabi-Yau threefolds (II) Morrison, David R.; Vafa, Cumrun Nuclear Physics B, Vol. 476, Issue 3 https://doi.org/10.1016/0550-3213(96)00369-0	journal	September 1996
Physics of F-theory compactifications without section Anderson, Lara B.; García-Etxebarria, Iñaki; Grimm, Thomas W. Journal of High Energy Physics, Vol. 2014, Issue 12 https://doi.org/10.1007/JHEP12(2014)156	journal	December 2014
F-theory vacua with $Z_{3}$ gauge symmetry Cvetič, Mirjam; Donagi, Ron; Klevers, Denis Nuclear Physics B, Vol. 898 https://doi.org/10.1016/j.nuclphysb.2015.07.011	journal	September 2015
Global aspects of the space of 6D $ \mathcal{N} = 1 $ supergravities Kumar, Vijay; Morrison, David R.; Taylor, Washington Journal of High Energy Physics, Vol. 2010, Issue 11 https://doi.org/10.1007/JHEP11(2010)118	journal	November 2010
An Abundance of K3 Fibrations from Polyhedra with Interchangeable Parts Candelas, Philip; Constantin, Andrei; Skarke, Harald Communications in Mathematical Physics, Vol. 324, Issue 3 https://doi.org/10.1007/s00220-013-1802-2	journal	October 2013
Classifying bases for 6D F-theory models Morrison, David; Taylor, Washington Open Physics, Vol. 10, Issue 5 https://doi.org/10.2478/s11534-012-0065-4	journal	January 2012
Toric bases for 6D F-theory models Morrison, D. R.; Taylor, W. Fortschritte der Physik, Vol. 60, Issue 11-12 https://doi.org/10.1002/prop.201200086	journal	May 2012
Non-toric bases for elliptic Calabi–Yau threefolds and 6D F-theory vacua Taylor, Washington; Wang, Yi-Nan Advances in Theoretical and Mathematical Physics, Vol. 21, Issue 4 https://doi.org/10.4310/ATMP.2017.v21.n4.a6	journal	January 2017
Calabi-Yau threefolds with large h 2,1 Johnson, Samuel B.; Taylor, Washington Journal of High Energy Physics, Vol. 2014, Issue 10 https://doi.org/10.1007/JHEP10(2014)023	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… Johnson, Samuel B.; Taylor, Washington Fortschritte der Physik, Vol. 64, Issue 8-9 https://doi.org/10.1002/prop.201600074	journal	August 2016
Duality between the webs of heterotic and type II vacua Candelasía Font, Philip Nuclear Physics B, Vol. 511, Issue 1-2 https://doi.org/10.1016/S0550-3213(96)00410-5	journal	February 1998
Geometric engineering in toric F-theory and GUTs with U(1) gauge factors Braun, Volker; Grimm, Thomas W.; Keitel, Jan Journal of High Energy Physics, Vol. 2013, Issue 12 https://doi.org/10.1007/JHEP12(2013)069	journal	December 2013
Scanning the skeleton of the 4D F-theory landscape Taylor, Washington; Wang, Yi-Nan Journal of High Energy Physics, Vol. 2018, Issue 1 https://doi.org/10.1007/JHEP01(2018)111	journal	January 2018
On Algebraic Fiber Space Structures on a Calabi-Yau 3-Fold Oguiso, Keiji International Journal of Mathematics, Vol. 04, Issue 03 https://doi.org/10.1142/S0129167X93000248	journal	June 1993
Algorithmic universality in F-theory compactifications Halverson, James; Long, Cody; Sung, Benjamin Physical Review D, Vol. 96, Issue 12 https://doi.org/10.1103/PhysRevD.96.126006	journal	December 2017
A new construction of Calabi–Yau manifolds: Generalized CICYs Anderson, Lara B.; Apruzzi, Fabio; Gao, Xin Amsterdam : Elsevier https://doi.org/10.15488/356	other	January 2016
F-Theory on all Toric Hypersurface Fibrations and its Higgs Branches Klevers, Denis; Pena, Damian Kaloni Mayorga; Oehlmann, Paul-Konstantin arXiv https://doi.org/10.48550/arxiv.1408.4808	text	January 2014
F-Theory Vacua with Z_3 Gauge Symmetry Cvetič, Mirjam; Donagi, Ron; Klevers, Denis arXiv https://doi.org/10.48550/arxiv.1502.06953	text	January 2015
Calabi-Yau 4-folds and toric fibrations Kreuzer, M.; Skarke, H. arXiv https://doi.org/10.48550/arxiv.hep-th/9701175	text	January 1997
String Dualities and Toric Geometry: An Introduction Skarke, Harald arXiv https://doi.org/10.48550/arxiv.hep-th/9806059	text	January 1998

Cited By (5)

Phases of 5d SCFTs from M-/F-theory on non-flat fibrations Apruzzi, Fabio; Lin, Ling; Mayrhofer, Christoph Journal of High Energy Physics, Vol. 2019, Issue 5 https://doi.org/10.1007/jhep05(2019)187	journal	May 2019
Modularity from monodromy Schimannek, Thorsten Journal of High Energy Physics, Vol. 2019, Issue 5 https://doi.org/10.1007/jhep05(2019)024	journal	May 2019
Topological strings on genus one fibered Calabi-Yau 3-folds and string dualities Cota, Cesar Fierro; Klemm, Albrecht; Schimannek, Thorsten Journal of High Energy Physics, Vol. 2019, Issue 11 https://doi.org/10.1007/jhep11(2019)170	journal	November 2019
Phases of 5d SCFTs from M-/F-theory on Non-Flat Fibrations Apruzzi, Fabio; Lin, Ling; Mayrhofer, Christoph arXiv https://doi.org/10.48550/arxiv.1811.12400	text	January 2018
Modularity from Monodromy Schimannek, Thorsten arXiv https://doi.org/10.48550/arxiv.1902.08215	text	January 2019

Similar Records

Comparing elliptic and toric hypersurface Calabi-Yau threefolds at large Hodge numbers

Journal Article · Thu Feb 14 00:00:00 EST 2019 · Journal of High Energy Physics (Online) · OSTI ID:1611866

Huang, Yu-Chien; Taylor, Washington

Fibration structure in toric hypersurface Calabi-Yau threefolds

Journal Article · Fri Mar 27 00:00:00 EDT 2020 · Journal of High Energy Physics (Online) · OSTI ID:1611866

Huang, Yu-Chien; Taylor, Washington

F-theory on all toric hypersurface fibrations and its Higgs branches

Journal Article · Tue Jan 27 00:00:00 EST 2015 · Journal of High Energy Physics (Online) · OSTI ID:1611866

Klevers, Denis; Mayorga Pena, Damian Kaloni; Oehlmann, Paul-Konstantin; +2 more

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Physics
Differential and Algebraic Geometry
F-Theory

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

Citation Formats

References (48)

Cited By (5)

Similar Records

Related Subjects