Instantons and Hilbert Functions

Understand

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 non-vanishing instanton superpotential.
• These show that non-vanishing 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 non-vanishing instanton superpotentials based on an affine Hilbert function.