# The F-theory geometry with most flux vacua

## Abstract

Applying the Ashok-Denef-Douglas estimation method to elliptic Calabi-Yau fourfolds suggests that a single elliptic fourfold M _{max} gives rise to O(10 ^{272,000}) F-theory flux vacua, and that the sum total of the numbers of flux vacua from all other F-theory geometries is suppressed by a relative factor of O(10 ^{–3000}). The fourfold M _{max} arises from a generic elliptic fibration over a specific toric threefold base B _{max}, and gives a geometrically non-Higgsable gauge group of E _{8} ^{9} × F _{4} ^{8} × (G _{2} × SU(2)) ^{16}, of which we expect some factors to be broken by G-flux to smaller groups. It is not possible to tune an SU(5) GUT group on any further divisors in M _{max}, or even an SU(2) or SU(3), so the standard model gauge group appears to arise in this context only from a broken E _{8} factor. Furthermore, the results of this paper can either be interpreted as providing a framework for predicting how the standard model arises most naturally in F-theory and the types of dark matter to be found in a typical F-theory compactification, or as a challenge to string theorists to explain why other choices of vacua are notmore »

- Authors:

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

- Publication Date:

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

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1237042

- Grant/Contract Number:
- SC0012567

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Volume: 2015; Journal Issue: 12; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; flux compactifications; F-Theory; superstring vacua

### Citation Formats

```
Taylor, Washington, and Wang, Yi -Nan.
```*The F-theory geometry with most flux vacua*. United States: N. p., 2015.
Web. doi:10.1007/JHEP12(2015)164.

```
Taylor, Washington, & Wang, Yi -Nan.
```*The F-theory geometry with most flux vacua*. United States. doi:10.1007/JHEP12(2015)164.

```
Taylor, Washington, and Wang, Yi -Nan. Mon .
"The F-theory geometry with most flux vacua". United States. doi:10.1007/JHEP12(2015)164. https://www.osti.gov/servlets/purl/1237042.
```

```
@article{osti_1237042,
```

title = {The F-theory geometry with most flux vacua},

author = {Taylor, Washington and Wang, Yi -Nan},

abstractNote = {Applying the Ashok-Denef-Douglas estimation method to elliptic Calabi-Yau fourfolds suggests that a single elliptic fourfold Mmax gives rise to O(10272,000) F-theory flux vacua, and that the sum total of the numbers of flux vacua from all other F-theory geometries is suppressed by a relative factor of O(10–3000). The fourfold Mmax arises from a generic elliptic fibration over a specific toric threefold base Bmax, and gives a geometrically non-Higgsable gauge group of E89 × F48 × (G 2 × SU(2))16, of which we expect some factors to be broken by G-flux to smaller groups. It is not possible to tune an SU(5) GUT group on any further divisors in Mmax, or even an SU(2) or SU(3), so the standard model gauge group appears to arise in this context only from a broken E8 factor. Furthermore, the results of this paper can either be interpreted as providing a framework for predicting how the standard model arises most naturally in F-theory and the types of dark matter to be found in a typical F-theory compactification, or as a challenge to string theorists to explain why other choices of vacua are not exponentially unlikely compared to F-theory compactifications on Mmax.},

doi = {10.1007/JHEP12(2015)164},

journal = {Journal of High Energy Physics (Online)},

issn = {1029-8479},

number = 12,

volume = 2015,

place = {United States},

year = {2015},

month = {12}

}

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