# Non-vanishing superpotentials in heterotic string theory and discrete torsion

## Abstract

Here, we study the non-perturbative superpotential in E8 E8 heterotic string theory on a non-simply connected Calabi-Yau manifold X, as well as on its simply connected covering space ~X . The superpotential is induced by the string wrapping holomorphic, isolated, genus 0 curves. According to the residue theorem of Beasley and Witten, the non-perturbative superpotential must vanish in a large class of heterotic vacua because the contributions from curves in the same homology class cancel each other. We point out, however, that in certain cases the curves treated in the residue theorem as lying in the same homology class, can actually have different area with respect to the physical Kahler form and can be in different homology classes. In these cases, the residue theorem is not directly applicable and the structure of the superpotential is more subtle. We also show, in a specific example, that the superpotential is non-zero both on ~X and on X. On the non-simply connected manifold X, we explicitly compute the leading contribution to the superpotential from all holomorphic, isolated, genus 0 curves with minimal area. Furthermore, the reason for the non-vanishing of the superpotental on X is that the second homology class contains a finitemore »

- Authors:

- Univ. of Western Australia, Crawley, WA (Australia). School of Physics
- 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:
- 1360741

- Grant/Contract Number:
- SC0007901

- 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: 1; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Superstring Vacua; Superstrings and Heterotic Strings

### Citation Formats

```
Buchbinder, Evgeny I., and Ovrut, Burt A..
```*Non-vanishing superpotentials in heterotic string theory and discrete torsion*. United States: N. p., 2017.
Web. doi:10.1007/JHEP01(2017)038.

```
Buchbinder, Evgeny I., & Ovrut, Burt A..
```*Non-vanishing superpotentials in heterotic string theory and discrete torsion*. United States. doi:10.1007/JHEP01(2017)038.

```
Buchbinder, Evgeny I., and Ovrut, Burt A.. Tue .
"Non-vanishing superpotentials in heterotic string theory and discrete torsion". United States.
doi:10.1007/JHEP01(2017)038. https://www.osti.gov/servlets/purl/1360741.
```

```
@article{osti_1360741,
```

title = {Non-vanishing superpotentials in heterotic string theory and discrete torsion},

author = {Buchbinder, Evgeny I. and Ovrut, Burt A.},

abstractNote = {Here, we study the non-perturbative superpotential in E8 E8 heterotic string theory on a non-simply connected Calabi-Yau manifold X, as well as on its simply connected covering space ~X . The superpotential is induced by the string wrapping holomorphic, isolated, genus 0 curves. According to the residue theorem of Beasley and Witten, the non-perturbative superpotential must vanish in a large class of heterotic vacua because the contributions from curves in the same homology class cancel each other. We point out, however, that in certain cases the curves treated in the residue theorem as lying in the same homology class, can actually have different area with respect to the physical Kahler form and can be in different homology classes. In these cases, the residue theorem is not directly applicable and the structure of the superpotential is more subtle. We also show, in a specific example, that the superpotential is non-zero both on ~X and on X. On the non-simply connected manifold X, we explicitly compute the leading contribution to the superpotential from all holomorphic, isolated, genus 0 curves with minimal area. Furthermore, the reason for the non-vanishing of the superpotental on X is that the second homology class contains a finite part called discrete torsion. As a result, the curves with the same area are distributed among different torsion classes and, hence, do not cancel each other},

doi = {10.1007/JHEP01(2017)038},

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

number = 1,

volume = 2017,

place = {United States},

year = {Tue Jan 10 00:00:00 EST 2017},

month = {Tue Jan 10 00:00:00 EST 2017}

}

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