A Monte Carlo exploration of threefold base geometries for 4d F-theory vacua
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Author(s)
Taylor, Washington
Wang, Yinan
Date Issued
January 2016
Journal
Journal of High Energy Physics
Publisher
Springer Berlin Heidelberg
Citation
Taylor, Washington, and Yi-Nan Wang. “A Monte Carlo Exploration of Threefold Base Geometries for 4d F-Theory Vacua.” Journal of High Energy Physics 2016.1 (2016): n. pag. © 2016 Springer International Publishing
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Final published version
Abstract
We use Monte Carlo methods to explore the set of toric threefold bases that support elliptic Calabi-Yau fourfolds for F-theory compactifications to four dimensions, and study the distribution of geometrically non-Higgsable gauge groups, matter, and quiver structure. We estimate the number of distinct threefold bases in the connected set studied to be ∼ 10[superscript 48]. The distribution of bases peaks around h [superscript 1,1] ∼ 82. All bases encountered after “thermalization” have some geometric non-Higgsable structure. We find that the number of non-Higgsable gauge group factors grows roughly linearly in h [superscript 1,1] of the threefold base. Typical bases have ∼ 6 isolated gauge factors as well as several larger connected clusters of gauge factors with jointly charged matter. Approximately 76% of the bases sampled contain connected two-factor gauge group products of the form SU(3) × SU(2), which may act as the non-Abelian part of the standard model gauge group. SU(3) × SU(2) is the third most common connected two-factor product group, following SU(2) × SU(2) and G 2 × SU(2), which arise more frequently.
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/JHEP01(2016)137
