# Abelian F-theory models with charge-3 and charge-4 matter

## Abstract

This paper analyzes U(1) F-theory models admitting matter with charges q = 3 and 4. First, we systematically derive a q = 3 construction that generalizes the previous q = 3 examples. We argue that U(1) symmetries can be tuned through a procedure reminiscent of the SU( *N*) and Sp( *N*) tuning process. For models with q = 3 matter, the components of the generating section vanish to orders higher than 1 at the charge-3 matter loci. As a result, the Weierstrass models can contain non-UFD structure and thereby deviate from the standard Morrison-Park form. Techniques used to tune SU( *N*) models on singular divisors allow us to determine the non-UFD structures and derive the q = 3 tuning from scratch. Here, we also obtain a class of a q=4 models by deforming a prior U(1) × U(1) construction. To the author’s knowledge, this is the first published F-theory example with charge-4 matter. Finally, we discuss some conjectures regarding models with charges larger than 4.

- Authors:

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

- Publication Date:

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

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

- OSTI Identifier:
- 1499039

- Grant/Contract Number:
- SC0012567

- Resource Type:
- Journal Article: Accepted Manuscript

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

- Additional Journal Information:
- Journal Volume: 2018; Journal Issue: 5; 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

```
Raghuram, Nikhil.
```*Abelian F-theory models with charge-3 and charge-4 matter*. United States: N. p., 2018.
Web. doi:10.1007/jhep05(2018)050.

```
Raghuram, Nikhil.
```*Abelian F-theory models with charge-3 and charge-4 matter*. United States. doi:10.1007/jhep05(2018)050.

```
Raghuram, Nikhil. Tue .
"Abelian F-theory models with charge-3 and charge-4 matter". United States. doi:10.1007/jhep05(2018)050. https://www.osti.gov/servlets/purl/1499039.
```

```
@article{osti_1499039,
```

title = {Abelian F-theory models with charge-3 and charge-4 matter},

author = {Raghuram, Nikhil},

abstractNote = {This paper analyzes U(1) F-theory models admitting matter with charges q = 3 and 4. First, we systematically derive a q = 3 construction that generalizes the previous q = 3 examples. We argue that U(1) symmetries can be tuned through a procedure reminiscent of the SU(N) and Sp(N) tuning process. For models with q = 3 matter, the components of the generating section vanish to orders higher than 1 at the charge-3 matter loci. As a result, the Weierstrass models can contain non-UFD structure and thereby deviate from the standard Morrison-Park form. Techniques used to tune SU(N) models on singular divisors allow us to determine the non-UFD structures and derive the q = 3 tuning from scratch. Here, we also obtain a class of a q=4 models by deforming a prior U(1) × U(1) construction. To the author’s knowledge, this is the first published F-theory example with charge-4 matter. Finally, we discuss some conjectures regarding models with charges larger than 4.},

doi = {10.1007/jhep05(2018)050},

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

issn = {1029-8479},

number = 5,

volume = 2018,

place = {United States},

year = {2018},

month = {5}

}