### 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 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.

Language | English |
---|---|

Article number | 32 |

Journal | Journal of High Energy Physics |

Volume | 2017 |

Issue number | 10 |

DOIs | |

State | Published - 1 Oct 2017 |

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*Journal of High Energy Physics*,

*2017*(10), [32]. DOI: 10.1007/JHEP10(2017)032

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*Journal of High Energy Physics*, vol 2017, no. 10, 32. DOI: 10.1007/JHEP10(2017)032

**Heterotic instanton superpotentials from complete intersection Calabi-Yau manifolds.** / Buchbinder, Evgeny; Lukas, Andre; Ovrut, Burt; Ruehle, Fabian.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Heterotic instanton superpotentials from complete intersection Calabi-Yau manifolds

AU - Buchbinder,Evgeny

AU - Lukas,Andre

AU - Ovrut,Burt

AU - Ruehle,Fabian

PY - 2017/10/1

Y1 - 2017/10/1

N2 - 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 ℙ1 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.

AB - 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 ℙ1 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.

KW - Flux compactifications

KW - Superstring Vacua

KW - Superstrings and Heterotic Strings

UR - http://www.scopus.com/inward/record.url?scp=85031306278&partnerID=8YFLogxK

U2 - 10.1007/JHEP10(2017)032

DO - 10.1007/JHEP10(2017)032

M3 - Article

VL - 2017

JO - JOURNAL OF HIGH ENERGY PHYSICS

T2 - JOURNAL OF HIGH ENERGY PHYSICS

JF - JOURNAL OF HIGH ENERGY PHYSICS

SN - 1029-8479

IS - 10

M1 - 32

ER -