Instantons and Hilbert functions

We study superpotentials from worldsheet instantons in heterotic Calabi-Yau compactifications for vector bundles constructed from line bundle sums, monads, and extensions. Within a certain class of manifolds and for certain second homology classes, we derive simple necessary conditions for a nonvani...

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Bibliographic Details
Published in:Physical review. D 2020-07, Vol.102 (2), p.1, Article 026019
Main Authors: Buchbinder, Evgeny I., Lukas, Andre, Ovrut, Burt A., Ruehle, Fabian
Format: Article
Language:English
Subjects:
Bundles
Bundling
Criteria
Homology
Instantons
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Summary:We study superpotentials from worldsheet instantons in heterotic Calabi-Yau compactifications for vector bundles constructed from line bundle sums, monads, and extensions. Within a certain class of manifolds and for certain second homology classes, we derive simple necessary conditions for a nonvanishing instanton superpotential. These show that nonvanishing instanton superpotentials are rare and require a specific pattern for the bundle construction. For the class of monad and extension bundles with this pattern, we derive a sufficient criterion for nonvanishing instanton superpotentials based on an affine Hilbert function. This criterion shows that a nonzero instanton superpotential is common within this class. The criterion can be checked using commutative algebra methods only and depends on the topological data defining the Calabi-Yau X and the vector bundle V.
ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.102.026019