Non-vanishing Heterotic Superpotentials on Elliptic Fibrations

TL;DR

This paper constructs heterotic string models on elliptic Calabi-Yau threefolds with unique genus-zero curves, explicitly calculating non-zero superpotentials from string instantons, thus advancing understanding of non-perturbative effects in string compactifications.

Contribution

It provides explicit heterotic compactification models with calculable non-vanishing superpotentials due to isolated genus-zero curves, avoiding the Beasley-Witten residue theorem.

Findings

Superpotentials are explicitly computed and shown to be non-zero.

Models are based on elliptic fibrations over del Pezzo surfaces.

The work explains how these models evade the Beasley-Witten theorem.

Abstract

We present models of heterotic compactification on Calabi-Yau threefolds and compute the non-perturbative superpotential for vector bundle moduli. The key feature of these models is that the threefolds, which are elliptically fibered over del Pezzo surfaces, have homology classes with a unique holomorphic, isolated genus-zero curve. Using the spectral cover construction, we present vector bundles for which we can explicitly calculate the Pfaffians associated with string instantons on these curves. These are shown to be non-zero, thus leading to a non-vanishing superpotential in the 4D effective action. We discuss, in detail, why such compactifications avoid the Beasley-Witten residue theorem.