High Energy Physics - Theory
[Submitted on 15 May 2018 (v1), last revised 4 May 2019 (this version, v6)]
Title:Comparing elliptic and toric hypersurface Calabi-Yau threefolds at large Hodge numbers
View PDFAbstract: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 $h^{2, 1}\geq 240$ 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.
Submission history
From: Yu-Chien Huang [view email][v1] Tue, 15 May 2018 17:00:18 UTC (347 KB)
[v2] Thu, 28 Jun 2018 08:52:46 UTC (347 KB)
[v3] Fri, 14 Sep 2018 12:48:23 UTC (347 KB)
[v4] Wed, 23 Jan 2019 19:18:35 UTC (339 KB)
[v5] Sun, 24 Feb 2019 04:34:47 UTC (339 KB)
[v6] Sat, 4 May 2019 12:06:40 UTC (340 KB)
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