Instantons and Hilbert functions

Evgeny I. Buchbinder, Andre Lukas, Burt A. Ovrut, Fabian Ruehle

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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.

Original languageEnglish
Article number026019
JournalPhysical Review D
Issue number2
Publication statusPublished - 15 Jul 2020


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