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Title: A Monte Carlo exploration of threefold base geometries for 4d F-theory vacua

Here, 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 48. Moreover, the distribution of bases peaks around h 1,1 ~ 82. All bases encountered after "thermalization" have some geometric non-Higgsable structure. We also find that the number of non-Higgsable gauge group factors grows roughly linearly in h 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) x SU(2), which may act as the non-Abelian part of the standard model gauge group. SU(3) x SU(2) is the third most common connected two-factor product group, following SU(2) x SU(2) and G2 x SU(2), which arise more frequently.
Authors:
 [1] ;  [1]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Center for Theoretical Physics
Publication Date:
Grant/Contract Number:
SC0012567
Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 1; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Research Org:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org:
USDOE Office of Science (SC)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 97 MATHEMATICS AND COMPUTING; F-theory; superstring; vacua
OSTI Identifier:
1327305

Taylor, Washington, and Wang, Yi-Nan. A Monte Carlo exploration of threefold base geometries for 4d F-theory vacua. United States: N. p., Web. doi:10.1007/JHEP01(2016)137.
Taylor, Washington, & Wang, Yi-Nan. A Monte Carlo exploration of threefold base geometries for 4d F-theory vacua. United States. doi:10.1007/JHEP01(2016)137.
Taylor, Washington, and Wang, Yi-Nan. 2016. "A Monte Carlo exploration of threefold base geometries for 4d F-theory vacua". United States. doi:10.1007/JHEP01(2016)137. https://www.osti.gov/servlets/purl/1327305.
@article{osti_1327305,
title = {A Monte Carlo exploration of threefold base geometries for 4d F-theory vacua},
author = {Taylor, Washington and Wang, Yi-Nan},
abstractNote = {Here, 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 ~ 1048. Moreover, the distribution of bases peaks around h1,1 ~ 82. All bases encountered after "thermalization" have some geometric non-Higgsable structure. We also find that the number of non-Higgsable gauge group factors grows roughly linearly in h1,1 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) x SU(2), which may act as the non-Abelian part of the standard model gauge group. SU(3) x SU(2) is the third most common connected two-factor product group, following SU(2) x SU(2) and G2 x SU(2), which arise more frequently.},
doi = {10.1007/JHEP01(2016)137},
journal = {Journal of High Energy Physics (Online)},
number = 1,
volume = 2016,
place = {United States},
year = {2016},
month = {1}
}