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

• Published in: The journal of high energy physics Vol. 2019; no. 2; pp. 1 - 93
• Main Authors: Huang, Yu-Chien, Taylor, Washington
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2019; Springer Nature B.V; Springer Berlin; SpringerOpen
• Subjects: Beyond Standard Model; Classical and Quantum Gravitation; Differential and Algebraic Geometry; Elementary Particles; F-Theory; Hadron-Hadron scattering (experiments); High energy physics; Hyperspaces; PARTICLE ACCELERATORS; Physics; Physics and Astronomy; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Superstring Vacua; Superstring Vacua; F-Theory; Differential and Algebraic Geometry
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP02(2019)087

A bstract 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.