# Type II string theory on Calabi-Yau manifolds with torsion and non-Abelian discrete gauge symmetries

## Abstract

Here, we provide the first explicit example of Type IIB string theory compactication on a globally defined Calabi-Yau threefold with torsion which results in a fourdimensional effective theory with a non-Abelian discrete gauge symmetry. Our example is based on a particular Calabi-Yau manifold, the quotient of a product of three elliptic curves by a fixed point free action of Z _{2} X Z _{2}. Its cohomology contains torsion classes in various degrees. The main technical novelty is in determining the multiplicative structure of the (torsion part of) the cohomology ring, and in particular showing that the cup product of second cohomology torsion elements goes non-trivially to the fourth cohomology. This specifies a non-Abelian, Heisenberg-type discrete symmetry group of the four-dimensional theory.

- Authors:

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

- Publication Date:

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

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1425671

- Grant/Contract Number:
- SC0013528; DMS 1603526; 390287

- 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: 7; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; String Field Theory; Conformal Field Models in String Theory; Discrete Symmetries

### Citation Formats

```
Braun, Volker, Cvetič, Mirjam, Donagi, Ron, and Poretschkin, Maximilian.
```*Type II string theory on Calabi-Yau manifolds with torsion and non-Abelian discrete gauge symmetries*. United States: N. p., 2017.
Web. doi:10.1007/JHEP07(2017)129.

```
Braun, Volker, Cvetič, Mirjam, Donagi, Ron, & Poretschkin, Maximilian.
```*Type II string theory on Calabi-Yau manifolds with torsion and non-Abelian discrete gauge symmetries*. United States. doi:10.1007/JHEP07(2017)129.

```
Braun, Volker, Cvetič, Mirjam, Donagi, Ron, and Poretschkin, Maximilian. Wed .
"Type II string theory on Calabi-Yau manifolds with torsion and non-Abelian discrete gauge symmetries". United States. doi:10.1007/JHEP07(2017)129. https://www.osti.gov/servlets/purl/1425671.
```

```
@article{osti_1425671,
```

title = {Type II string theory on Calabi-Yau manifolds with torsion and non-Abelian discrete gauge symmetries},

author = {Braun, Volker and Cvetič, Mirjam and Donagi, Ron and Poretschkin, Maximilian},

abstractNote = {Here, we provide the first explicit example of Type IIB string theory compactication on a globally defined Calabi-Yau threefold with torsion which results in a fourdimensional effective theory with a non-Abelian discrete gauge symmetry. Our example is based on a particular Calabi-Yau manifold, the quotient of a product of three elliptic curves by a fixed point free action of Z2 X Z2. Its cohomology contains torsion classes in various degrees. The main technical novelty is in determining the multiplicative structure of the (torsion part of) the cohomology ring, and in particular showing that the cup product of second cohomology torsion elements goes non-trivially to the fourth cohomology. This specifies a non-Abelian, Heisenberg-type discrete symmetry group of the four-dimensional theory.},

doi = {10.1007/JHEP07(2017)129},

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

number = 7,

volume = 2017,

place = {United States},

year = {Wed Jul 26 00:00:00 EDT 2017},

month = {Wed Jul 26 00:00:00 EDT 2017}

}

*Citation information provided by*

Web of Science

Web of Science