A Monte Carlo exploration of threefold base geometries for 4d Ftheory vacua
Here, we use Monte Carlo methods to explore the set of toric threefold bases that support elliptic CalabiYau fourfolds for Ftheory compactifications to four dimensions, and study the distribution of geometrically nonHiggsable 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 nonHiggsable structure. We also find that the number of nonHiggsable 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 twofactor gauge group products of the form SU(3) x SU(2), which may act as the nonAbelian part of the standard model gauge group. SU(3) x SU(2) is the third most common connected twofactor product group, following SU(2) x SU(2) and G2 x SU(2), which arise more frequently.
 Authors:

^{[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 10298479
 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; Ftheory; superstring; vacua
 OSTI Identifier:
 1327305
Taylor, Washington, and Wang, YiNan. A Monte Carlo exploration of threefold base geometries for 4d Ftheory vacua. United States: N. p.,
Web. doi:10.1007/JHEP01(2016)137.
Taylor, Washington, & Wang, YiNan. A Monte Carlo exploration of threefold base geometries for 4d Ftheory vacua. United States. doi:10.1007/JHEP01(2016)137.
Taylor, Washington, and Wang, YiNan. 2016.
"A Monte Carlo exploration of threefold base geometries for 4d Ftheory 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 Ftheory vacua},
author = {Taylor, Washington and Wang, YiNan},
abstractNote = {Here, we use Monte Carlo methods to explore the set of toric threefold bases that support elliptic CalabiYau fourfolds for Ftheory compactifications to four dimensions, and study the distribution of geometrically nonHiggsable 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 nonHiggsable structure. We also find that the number of nonHiggsable 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 twofactor gauge group products of the form SU(3) x SU(2), which may act as the nonAbelian part of the standard model gauge group. SU(3) x SU(2) is the third most common connected twofactor 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}
}