Heterotic Instantons for Monad and Extension Bundles

TL;DR

This paper develops geometric methods to compute non-perturbative superpotentials from world-sheet instantons in heterotic string theory with monad and extension bundles, exploring conditions for their vanishing or non-vanishing.

Contribution

It introduces new geometric techniques for calculating instanton superpotentials in heterotic string theory with specific bundles, and tests their implications using gauged linear sigma models.

Findings

Identifies examples with non-vanishing superpotentials.

Supports the idea that non-compact instanton moduli spaces relate to superpotential vanishing.

Finds cases where Pfaffians are linearly dependent despite non-compact moduli spaces.

Abstract

We consider non-perturbative superpotentials from world-sheet instantons wrapped on holomorphic genus zero curves in heterotic string theory. These superpotential contributions feature prominently in moduli stabilization and large field axion inflation, which makes their presence or absence, as well as their functional dependence on moduli, an important issue. We develop geometric methods to compute the instanton superpotentials for heterotic string theory with monad and extension bundles. Using our methods, we find a variety of examples with a non-vanishing superpotential. In view of standard vanishing theorems, we speculate that these results are likely to be attributed to the non-compactness of the instanton moduli space. We test this proposal, for the case of monad bundles, by considering gauged linear sigma models where compactness of the instanton moduli space can be explicitly checked. In all such cases, we find that the geometric results are consistent with the vanishing theorems. Surprisingly, linearly dependent Pfaffians even arise for cases with a non-compact instanton moduli space. This suggests some gauged linear sigma models with a non-compact instanton moduli space may still have a vanishing instanton superpotential.