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Title: Scanning the skeleton of the 4D F-theory landscape

Using a one-way Monte Carlo algorithm from several different starting points, we get an approximation to the distribution of toric threefold bases that can be used in four-dimensional F-theory compactification. We separate the threefold bases into “resolvable” ones where the Weierstrass polynomials (f, g) can vanish to order (4, 6) or higher on codimension-two 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 Calabi-Yau fourfolds with specific Hodge numbers mirror to elliptic fibrations over simple threefolds. The non-Higgsable 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 non-Higgsable SU(3). Moreover, by randomly contracting the end point bases, we find many resolvable bases with h 1,1(B) ~ 50-200 that cannot be contracted to anothermore » smooth threefold base.« less
Authors:
 [1] ;  [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 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:
97 MATHEMATICS AND COMPUTING; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Differential and Algebraic Geometry; F-Theory; Superstring Vacua
OSTI Identifier:
1505566

Taylor, Washington, and Wang, Yi-Nan. Scanning the skeleton of the 4D F-theory landscape. United States: N. p., Web. doi:10.1007/jhep01(2018)111.
Taylor, Washington, & Wang, Yi-Nan. Scanning the skeleton of the 4D F-theory landscape. United States. doi:10.1007/jhep01(2018)111.
Taylor, Washington, and Wang, Yi-Nan. 2018. "Scanning the skeleton of the 4D F-theory 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 F-theory landscape},
author = {Taylor, Washington and Wang, Yi-Nan},
abstractNote = {Using a one-way Monte Carlo algorithm from several different starting points, we get an approximation to the distribution of toric threefold bases that can be used in four-dimensional F-theory compactification. We separate the threefold bases into “resolvable” ones where the Weierstrass polynomials (f, g) can vanish to order (4, 6) or higher on codimension-two 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 Calabi-Yau fourfolds with specific Hodge numbers mirror to elliptic fibrations over simple threefolds. The non-Higgsable 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 non-Higgsable SU(3). Moreover, by randomly contracting the end point bases, we find many resolvable bases with h1,1(B) ~ 50-200 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}
}