Scanning the skeleton of the 4D Ftheory landscape
Using a oneway Monte Carlo algorithm from several different starting points, we get an approximation to the distribution of toric threefold bases that can be used in fourdimensional Ftheory compactification. We separate the threefold bases into “resolvable” ones where the Weierstrass polynomials (f, g) can vanish to order (4, 6) or higher on codimensiontwo loci and the “good” bases where these (4, 6) loci are not allowed. A simple estimate suggests that the number of distinct resolvable base geometries exceeds 10 ^{3000}, with over 10 ^{250} “good” bases, though the actual numbers are likely much larger. We find that the good bases are concentrated at specific “end points” with special isolated values of h ^{1,1} that are bigger than 1,000. These end point bases give CalabiYau fourfolds with specific Hodge numbers mirror to elliptic fibrations over simple threefolds. The nonHiggsable gauge groups on the end point bases are almost entirely made of products of E _{8}, F _{4}, G _{2} and SU(2). Nonetheless, we find a large class of good bases with a single nonHiggsable SU(3). Moreover, by randomly contracting the end point bases, we find many resolvable bases with h ^{1,1}(B) ~ 50200 that cannot be contracted to anothermore »
 Authors:

^{[1]};
^{[1]}
 Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Center for Theoretical Physics, Dept. of 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: 2018; 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:
 97 MATHEMATICS AND COMPUTING; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Differential and Algebraic Geometry; FTheory; Superstring Vacua
 OSTI Identifier:
 1505566
Taylor, Washington, and Wang, YiNan. Scanning the skeleton of the 4D Ftheory landscape. United States: N. p.,
Web. doi:10.1007/jhep01(2018)111.
Taylor, Washington, & Wang, YiNan. Scanning the skeleton of the 4D Ftheory landscape. United States. doi:10.1007/jhep01(2018)111.
Taylor, Washington, and Wang, YiNan. 2018.
"Scanning the skeleton of the 4D Ftheory landscape". United States.
doi:10.1007/jhep01(2018)111. https://www.osti.gov/servlets/purl/1505566.
@article{osti_1505566,
title = {Scanning the skeleton of the 4D Ftheory landscape},
author = {Taylor, Washington and Wang, YiNan},
abstractNote = {Using a oneway Monte Carlo algorithm from several different starting points, we get an approximation to the distribution of toric threefold bases that can be used in fourdimensional Ftheory compactification. We separate the threefold bases into “resolvable” ones where the Weierstrass polynomials (f, g) can vanish to order (4, 6) or higher on codimensiontwo loci and the “good” bases where these (4, 6) loci are not allowed. A simple estimate suggests that the number of distinct resolvable base geometries exceeds 103000, with over 10250 “good” bases, though the actual numbers are likely much larger. We find that the good bases are concentrated at specific “end points” with special isolated values of h1,1 that are bigger than 1,000. These end point bases give CalabiYau fourfolds with specific Hodge numbers mirror to elliptic fibrations over simple threefolds. The nonHiggsable gauge groups on the end point bases are almost entirely made of products of E8, F4, G2 and SU(2). Nonetheless, we find a large class of good bases with a single nonHiggsable SU(3). Moreover, by randomly contracting the end point bases, we find many resolvable bases with h1,1(B) ~ 50200 that cannot be contracted to another smooth threefold base.},
doi = {10.1007/jhep01(2018)111},
journal = {Journal of High Energy Physics (Online)},
number = 1,
volume = 2018,
place = {United States},
year = {2018},
month = {1}
}