## The global gauge group structure of F-theory compactification with U(1)s

## Abstract

We show that F-theory compactifications with abelian gauge factors generally exhibit a non-trivial global gauge group structure. The geometric origin of this structure lies with the Shioda map of the Mordell-Weil generators. This results in constraints on the u(1) charges of non-abelian matter consistent with observations made throughout the literature. Specifically, we find that F-theory models featuring the Standard Model algebra actually realise the precise gauge group [SU( _{3}) × SU( _{2}) × U( _{1})]/Ζ _{6}. Furthermore, we explore the relationship between the gauge group structure and geometric (un-)higgsing. In an explicit class of models, we show that, depending on the global group structure, an su(2)⊕u(1) gauge theory can either unhiggs into an SU( _{2}) × SU( _{2}) or an SU( _{3}) × SU( _{2}) theory. We also study implications of the charge constraints as a criterion for the F-theory ‘swampland’.

- Authors:

- Univ. of Pennsylvania, Philadelphia, PA (United States). Dept. of Physics and Astronomy; Univ. of Maribor, Maribor (Slovenia). Center for Applied Mathematics and Theoretical Physics
- Univ. of Pennsylvania, Philadelphia, PA (United States). Dept. of Physics and Astronomy

- Publication Date:

- Research Org.:
- Univ. of Pennsylvania, Philadelphia (United States)

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

- OSTI Identifier:
- 1498531

- Grant/Contract Number:
- SC0013528

- 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: 2018; 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; F-Theory; Compactification and String Models; Gauge Symmetry

### Citation Formats

```
Cvetič, Mirjam, and Lin, Ling. The global gauge group structure of F-theory compactification with U(1)s. United States: N. p., 2018.
Web. doi:10.1007/jhep01(2018)157.
```

```
Cvetič, Mirjam, & Lin, Ling. The global gauge group structure of F-theory compactification with U(1)s. United States. doi:10.1007/jhep01(2018)157.
```

```
Cvetič, Mirjam, and Lin, Ling. Wed .
"The global gauge group structure of F-theory compactification with U(1)s". United States. doi:10.1007/jhep01(2018)157. https://www.osti.gov/servlets/purl/1498531.
```

```
@article{osti_1498531,
```

title = {The global gauge group structure of F-theory compactification with U(1)s},

author = {Cvetič, Mirjam and Lin, Ling},

abstractNote = {We show that F-theory compactifications with abelian gauge factors generally exhibit a non-trivial global gauge group structure. The geometric origin of this structure lies with the Shioda map of the Mordell-Weil generators. This results in constraints on the u(1) charges of non-abelian matter consistent with observations made throughout the literature. Specifically, we find that F-theory models featuring the Standard Model algebra actually realise the precise gauge group [SU(3) × SU(2) × U(1)]/Ζ6. Furthermore, we explore the relationship between the gauge group structure and geometric (un-)higgsing. In an explicit class of models, we show that, depending on the global group structure, an su(2)⊕u(1) gauge theory can either unhiggs into an SU(2) × SU(2) or an SU(3) × SU(2) theory. We also study implications of the charge constraints as a criterion for the F-theory ‘swampland’.},

doi = {10.1007/jhep01(2018)157},

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

number = 1,

volume = 2018,

place = {United States},

year = {2018},

month = {1}

}