# Discrete symmetries in Heterotic/F-theory duality and mirror symmetry

## Abstract

We study aspects of Heterotic/F-theory duality for compacti cations with Abelian discrete gauge symmetries. We consider F-theory compacti cations on genus-one bered Calabi-Yau manifolds with n-sections, associated with the Tate-Shafarevich group Z _{n}. Such models are obtained by studying rst a speci c toric set-up whose associated Heterotic vector bundle has structure group Z _{n}. By employing a conjectured Heterotic/Ftheory mirror symmetry we construct dual geometries of these original toric models, where in the stable degeneration limit we obtain a discrete gauge symmetry of order two and three, for compacti cations to six dimensions. We provide explicit constructions of mirrorpairs for symmetric examples with Z _{2} and Z _{3}, in six dimensions. The Heterotic models with symmetric discrete symmetries are related in eld theory to a Higgsing of Heterotic models with two symmetric abelian U(1) gauge factors, where due to the Stuckelberg mechanism only a diagonal U(1) factor remains massless, and thus after Higgsing only a diagonal discrete symmetry of order n is present in the Heterotic models and detected via Heterotic/F-theory duality. These constructions also provide further evidence for the conjectured mirror symmetry in Heterotic/F-theory at the level of brations with torsional sections and those with multi-sections.

- Authors:

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

- Publication Date:

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

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1425672

- Grant/Contract Number:
- SC0013528

- Resource Type:
- Journal Article: Accepted Manuscript

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

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 6; 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; Discrete Symmetries; F-theory; String Duality; Superstrings; Heterotic Strings

### Citation Formats

```
Cvetič, Mirjam, Grassi, Antonella, and Poretschkin, Maximilian.
```*Discrete symmetries in Heterotic/F-theory duality and mirror symmetry*. United States: N. p., 2017.
Web. doi:10.1007/JHEP06(2017)156.

```
Cvetič, Mirjam, Grassi, Antonella, & Poretschkin, Maximilian.
```*Discrete symmetries in Heterotic/F-theory duality and mirror symmetry*. United States. doi:10.1007/JHEP06(2017)156.

```
Cvetič, Mirjam, Grassi, Antonella, and Poretschkin, Maximilian. Fri .
"Discrete symmetries in Heterotic/F-theory duality and mirror symmetry". United States.
doi:10.1007/JHEP06(2017)156. https://www.osti.gov/servlets/purl/1425672.
```

```
@article{osti_1425672,
```

title = {Discrete symmetries in Heterotic/F-theory duality and mirror symmetry},

author = {Cvetič, Mirjam and Grassi, Antonella and Poretschkin, Maximilian},

abstractNote = {We study aspects of Heterotic/F-theory duality for compacti cations with Abelian discrete gauge symmetries. We consider F-theory compacti cations on genus-one bered Calabi-Yau manifolds with n-sections, associated with the Tate-Shafarevich group Zn. Such models are obtained by studying rst a speci c toric set-up whose associated Heterotic vector bundle has structure group Zn. By employing a conjectured Heterotic/Ftheory mirror symmetry we construct dual geometries of these original toric models, where in the stable degeneration limit we obtain a discrete gauge symmetry of order two and three, for compacti cations to six dimensions. We provide explicit constructions of mirrorpairs for symmetric examples with Z2 and Z3, in six dimensions. The Heterotic models with symmetric discrete symmetries are related in eld theory to a Higgsing of Heterotic models with two symmetric abelian U(1) gauge factors, where due to the Stuckelberg mechanism only a diagonal U(1) factor remains massless, and thus after Higgsing only a diagonal discrete symmetry of order n is present in the Heterotic models and detected via Heterotic/F-theory duality. These constructions also provide further evidence for the conjectured mirror symmetry in Heterotic/F-theory at the level of brations with torsional sections and those with multi-sections.},

doi = {10.1007/JHEP06(2017)156},

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

number = 6,

volume = 2017,

place = {United States},

year = {Fri Jun 30 00:00:00 EDT 2017},

month = {Fri Jun 30 00:00:00 EDT 2017}

}

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