Comparing elliptic and toric hypersurface Calabi-Yau threefolds at large Hodge numbers
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Author(s)
Huang, Yu-Chien
Taylor IV, Washington
Date Issued
February 2019
Journal
Journal of High Energy Physics
Publisher
Springer Berlin Heidelberg
Citation
Huang, Yu-Chien, and Washington Taylor. “Comparing Elliptic and Toric Hypersurface Calabi-Yau Threefolds at Large Hodge Numbers.” Journal of High Energy Physics, vol. 2019, no. 2, Feb. 2019. © The Authors
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Final published version
Abstract
We compare the sets of Calabi-Yau 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 F-theory. 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[superscript 1,1], h[superscript 2,1]) with h[superscript 1,1] or h[superscript 2,1] ≥ 240 that are associated with threefolds in the Kreuzer-Skarke 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 non-toric bases, models with new Tate tunings that can give rise to exotic matter in the 6D F-theory picture, tunings of gauge groups over non-toric curves, tunings with very large Hodge number shifts and associated nonabelian gauge groups, and tuned Mordell-Weil sections associated with U(1) factors in the corresponding 6D theory. Keywords: Differential and Algebraic Geometry, F-Theory, Superstring Vacua
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1007/JHEP02(2019)087
