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

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 1,1, h 2,1) with h 1,1 or h 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.

Authors:
 [1];  [1]
  1. 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 1029-8479
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; Hadron-Hadron scattering (experiments)

Citation Formats

Huang, Yu-Chien, and Taylor, Washington. Comparing elliptic and toric hypersurface Calabi-Yau threefolds at large Hodge numbers. United States: N. p., 2019. Web. doi:10.1007/jhep02(2019)087.
Huang, Yu-Chien, & Taylor, Washington. Comparing elliptic and toric hypersurface Calabi-Yau threefolds at large Hodge numbers. United States. doi:10.1007/jhep02(2019)087.
Huang, Yu-Chien, and Taylor, Washington. Thu . "Comparing elliptic and toric hypersurface Calabi-Yau 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 Calabi-Yau threefolds at large Hodge numbers},
author = {Huang, Yu-Chien and Taylor, Washington},
abstractNote = {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 (h1,1, h2,1) with h1,1 or h2,1 ≥ 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.},
doi = {10.1007/jhep02(2019)087},
journal = {Journal of High Energy Physics (Online)},
issn = {1029-8479},
number = 2,
volume = 2019,
place = {United States},
year = {2019},
month = {2}
}

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Cited by: 9 works
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