# Heterotic instanton superpotentials from complete intersection Calabi-Yau manifolds

## Abstract

We study Pfaffians that appear in non-perturbative superpotential terms arising from worldsheet instantons in heterotic theories. A result by Beasley and Witten shows that these instanton contributions cancel among curves within a given homology class for Calabi-Yau manifolds that can be described as hypersurfaces or complete intersections in projective or toric ambient spaces. We provide a prescription that identifies all $$\mathbb{P}$$ ^{1} curves in certain homology classes of complete intersection Calabi-Yau manifolds in products of projective spaces (CICYs) and cross-check our results by a comparison with the genus zero Gromov-Witten invariants. We then use this construction to study instanton superpotentials on those manifolds and their quotients. We identify a non-toric quotient of a non-favorable CICY with a single genus zero curve in a certain homology class, so that a cancellation à la Beasley-Witten is not possible. In another example, we study a non-toric quotient of a favorable CICY and check that the superpotential still vanishes. From this and related examples, we conjecture that the Beasley-Witten cancellation result can be extended to toric and non-toric quotients of CICYs, but can be avoided if the CICY is non-favorable.

- Authors:

- Univ. of Western Australia, Crawley, WA (Australia). School of Physics and Astronomy
- Univ. of Oxford (United Kingdom). Rudolf Peierls Centre for Theoretical 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 Office of Science (SC)

- OSTI Identifier:
- 1505205

- Grant/Contract Number:
- SC0007901

- Resource Type:
- Journal Article: Accepted Manuscript

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

- Additional Journal Information:
- Journal Volume: 2017; Journal Issue: 10; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

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

### Citation Formats

```
Buchbinder, Evgeny, Lukas, Andre, Ovrut, Burt, and Ruehle, Fabian.
```*Heterotic instanton superpotentials from complete intersection Calabi-Yau manifolds*. United States: N. p., 2017.
Web. doi:10.1007/jhep10(2017)032.

```
Buchbinder, Evgeny, Lukas, Andre, Ovrut, Burt, & Ruehle, Fabian.
```*Heterotic instanton superpotentials from complete intersection Calabi-Yau manifolds*. United States. doi:10.1007/jhep10(2017)032.

```
Buchbinder, Evgeny, Lukas, Andre, Ovrut, Burt, and Ruehle, Fabian. Wed .
"Heterotic instanton superpotentials from complete intersection Calabi-Yau manifolds". United States. doi:10.1007/jhep10(2017)032. https://www.osti.gov/servlets/purl/1505205.
```

```
@article{osti_1505205,
```

title = {Heterotic instanton superpotentials from complete intersection Calabi-Yau manifolds},

author = {Buchbinder, Evgeny and Lukas, Andre and Ovrut, Burt and Ruehle, Fabian},

abstractNote = {We study Pfaffians that appear in non-perturbative superpotential terms arising from worldsheet instantons in heterotic theories. A result by Beasley and Witten shows that these instanton contributions cancel among curves within a given homology class for Calabi-Yau manifolds that can be described as hypersurfaces or complete intersections in projective or toric ambient spaces. We provide a prescription that identifies all $\mathbb{P}$1 curves in certain homology classes of complete intersection Calabi-Yau manifolds in products of projective spaces (CICYs) and cross-check our results by a comparison with the genus zero Gromov-Witten invariants. We then use this construction to study instanton superpotentials on those manifolds and their quotients. We identify a non-toric quotient of a non-favorable CICY with a single genus zero curve in a certain homology class, so that a cancellation à la Beasley-Witten is not possible. In another example, we study a non-toric quotient of a favorable CICY and check that the superpotential still vanishes. From this and related examples, we conjecture that the Beasley-Witten cancellation result can be extended to toric and non-toric quotients of CICYs, but can be avoided if the CICY is non-favorable.},

doi = {10.1007/jhep10(2017)032},

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

issn = {1029-8479},

number = 10,

volume = 2017,

place = {United States},

year = {2017},

month = {10}

}