# When rational sections become cyclic — Gauge enhancement in F-theory via Mordell-Weil torsion

## Abstract

We explore novel gauge enhancements from abelian to non-simply-connected gauge groups in F-theory. Accordingly, we consider complex structure deformations of elliptic fibrations with a Mordell-Weil group of rank one and identify the conditions under which the generating section becomes torsional. In the specific case of Ζ _{2} torsion we construct the generic solution to these conditions and show that the associated F-theory compactification exhibits the global gauge group [SU _{(2)} × SU _{(4)}]/Ζ _{2} × SU _{(2)}. The subsolution with gauge group SU _{(2)}/Ζ _{2} × SU _{(2)}, for which we provide a global resolution, is related by a further complex structure deformation to a genus-one fibration with a bisection whose Jacobian has a Ζ _{2} torsional section. While an analysis of the spectrum on the Jacobian fibration reveals an SU _{(2)}/Ζ _{2} × Ζ _{2} gauge theory, reproducing this result from the bisection geometry raises some conceptual puzzles about F-theory on genus-one fibrations.

- Authors:

- Heidelberg Univ., Heidelberg (Germany). Inst. for Theoretische Physik
- 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:
- 1498535

- Grant/Contract Number:
- SC0013528

- Resource Type:
- Journal Article: Accepted Manuscript

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

- Additional Journal Information:
- Journal Volume: 2018; Journal Issue: 3; 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; Superstring Vacua

### Citation Formats

```
Baume, Florent, Cvetič, Mirjam, Lawrie, Craig, and Lin, Ling.
```*When rational sections become cyclic — Gauge enhancement in F-theory via Mordell-Weil torsion*. United States: N. p., 2018.
Web. doi:10.1007/jhep03(2018)069.

```
Baume, Florent, Cvetič, Mirjam, Lawrie, Craig, & Lin, Ling.
```*When rational sections become cyclic — Gauge enhancement in F-theory via Mordell-Weil torsion*. United States. doi:10.1007/jhep03(2018)069.

```
Baume, Florent, Cvetič, Mirjam, Lawrie, Craig, and Lin, Ling. Mon .
"When rational sections become cyclic — Gauge enhancement in F-theory via Mordell-Weil torsion". United States. doi:10.1007/jhep03(2018)069. https://www.osti.gov/servlets/purl/1498535.
```

```
@article{osti_1498535,
```

title = {When rational sections become cyclic — Gauge enhancement in F-theory via Mordell-Weil torsion},

author = {Baume, Florent and Cvetič, Mirjam and Lawrie, Craig and Lin, Ling},

abstractNote = {We explore novel gauge enhancements from abelian to non-simply-connected gauge groups in F-theory. Accordingly, we consider complex structure deformations of elliptic fibrations with a Mordell-Weil group of rank one and identify the conditions under which the generating section becomes torsional. In the specific case of Ζ2 torsion we construct the generic solution to these conditions and show that the associated F-theory compactification exhibits the global gauge group [SU(2) × SU(4)]/Ζ2 × SU(2). The subsolution with gauge group SU(2)/Ζ2 × SU(2), for which we provide a global resolution, is related by a further complex structure deformation to a genus-one fibration with a bisection whose Jacobian has a Ζ2 torsional section. While an analysis of the spectrum on the Jacobian fibration reveals an SU(2)/Ζ2 × Ζ2 gauge theory, reproducing this result from the bisection geometry raises some conceptual puzzles about F-theory on genus-one fibrations.},

doi = {10.1007/jhep03(2018)069},

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

issn = {1029-8479},

number = 3,

volume = 2018,

place = {United States},

year = {2018},

month = {3}

}