Comparing elliptic and toric hypersurface CalabiYau threefolds at large Hodge numbers
Abstract
We compare the sets of CalabiYau threefolds with large Hodge numbers that are constructed using toric hypersurface methods with those can be constructed as elliptic fibrations using Weierstrass model techniques motivated by Ftheory. There is a close correspondence between the structure of “tops” in the toric polytope construction and Tate form tunings of Weierstrass models for elliptic fibrations. We find that all of the Hodge number pairs ( h ^{1,1}, h ^{2,1}) with h ^{1,1} or h ^{2,1} ≥ 240 that are associated with threefolds in the KreuzerSkarke database can be realized explicitly by generic or tuned Weierstrass/Tate models for elliptic fibrations over complex base surfaces. This includes a relatively small number of somewhat exotic constructions, including elliptic fibrations over nontoric bases, models with new Tate tunings that can give rise to exotic matter in the 6D Ftheory picture, tunings of gauge groups over nontoric curves, tunings with very large Hodge number shifts and associated nonabelian gauge groups, and tuned MordellWeil sections associated with U(1) factors in the corresponding 6D theory.
 Authors:

 Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
 Publication Date:
 Research Org.:
 Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), High Energy Physics (HEP)
 OSTI Identifier:
 1611865
 Grant/Contract Number:
 SC0012567
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Volume: 2019; Journal Issue: 2; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 43 PARTICLE ACCELERATORS; Physics; Beyond Standard Model; HadronHadron scattering (experiments)
Citation Formats
Huang, YuChien, and Taylor, Washington. Comparing elliptic and toric hypersurface CalabiYau threefolds at large Hodge numbers. United States: N. p., 2019.
Web. doi:10.1007/jhep02(2019)087.
Huang, YuChien, & Taylor, Washington. Comparing elliptic and toric hypersurface CalabiYau threefolds at large Hodge numbers. United States. doi:10.1007/jhep02(2019)087.
Huang, YuChien, and Taylor, Washington. Thu .
"Comparing elliptic and toric hypersurface CalabiYau threefolds at large Hodge numbers". United States. doi:10.1007/jhep02(2019)087. https://www.osti.gov/servlets/purl/1611865.
@article{osti_1611865,
title = {Comparing elliptic and toric hypersurface CalabiYau threefolds at large Hodge numbers},
author = {Huang, YuChien and Taylor, Washington},
abstractNote = {We compare the sets of CalabiYau threefolds with large Hodge numbers that are constructed using toric hypersurface methods with those can be constructed as elliptic fibrations using Weierstrass model techniques motivated by Ftheory. There is a close correspondence between the structure of “tops” in the toric polytope construction and Tate form tunings of Weierstrass models for elliptic fibrations. We find that all of the Hodge number pairs (h1,1, h2,1) with h1,1 or h2,1 ≥ 240 that are associated with threefolds in the KreuzerSkarke database can be realized explicitly by generic or tuned Weierstrass/Tate models for elliptic fibrations over complex base surfaces. This includes a relatively small number of somewhat exotic constructions, including elliptic fibrations over nontoric bases, models with new Tate tunings that can give rise to exotic matter in the 6D Ftheory picture, tunings of gauge groups over nontoric curves, tunings with very large Hodge number shifts and associated nonabelian gauge groups, and tuned MordellWeil sections associated with U(1) factors in the corresponding 6D theory.},
doi = {10.1007/jhep02(2019)087},
journal = {Journal of High Energy Physics (Online)},
issn = {10298479},
number = 2,
volume = 2019,
place = {United States},
year = {2019},
month = {2}
}
Web of Science
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