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Heterotic instanton superpotentials from complete intersection Calabi-Yau manifolds. (English) Zbl 1383.83158
Summary: We study Pfaffians that appear in non-perturbative superpotential terms arising from worldsheet instantons in heterotic theories. A result by C. Beasley and E. Witten [“On the origin of gravity and the laws of Newton”, Preprint, arXiv:hep-th/0304115] 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 a 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.

MSC:
83E30 String and superstring theories in gravitational theory
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
32Q25 Calabi-Yau theory (complex-analytic aspects)
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
Software:
CICY Quotients
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