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

## Abstract

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:

- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Center for Theoretical Physics

- Publication Date:

- Research Org.:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1327305

- Grant/Contract Number:
- SC0012567

- Resource 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

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 97 MATHEMATICS AND COMPUTING; F-theory; superstring; vacua

### Citation Formats

```
Taylor, Washington, and Wang, Yi-Nan. A Monte Carlo exploration of threefold base geometries for 4d F-theory vacua. United States: N. p., 2016.
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. Fri .
"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}

}

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