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.

25 pages, 3 figures

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• Infinitely Many M2-instanton Corrections to M-theory on $G_2$-manifolds
• Instantons and Hilbert Functions
• Non-vanishing Heterotic Superpotentials on Elliptic Fibrations
• Heterotic Instantons for Monad and Extension Bundles
• Numerical spectra of the Laplacian for line bundles on Calabi-Yau hypersurfaces
• Eigenvalues and eigenforms on Calabi-Yau threefolds
• Line Bundle Hidden Sectors for Strongly Coupled Heterotic Standard Models