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.

中文翻译：

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单子和扩展包的异质瞬间子

我们考虑了异质弦理论中包裹在全纯属零曲线上的世界片瞬子的非微扰超势。这些超电势贡献在模量稳定和大场轴膨胀方面具有突出特点，这使得它们的存在与否，以及它们对模量的功能依赖性成为一个重要问题。我们开发了几何方法来计算具有单子和可拓丛的异质弦理论的瞬时超势。使用我们的方法，我们找到了各种具有非零超电势的例子。鉴于标准消失定理，我们推测这些结果很可能归因于瞬子模空间的非紧凑性。我们测试这个提议，对于 monad bundles，通过考虑可以明确检查瞬时子模空间的紧凑性的规范线性 sigma 模型。在所有这些情况下，我们发现几何结果与消失定理一致。令人惊讶的是，线性相关的 Pfaffians 甚至出现在非紧致瞬子模空间的情况下。这表明一些具有非紧致瞬子模空间的测量线性 sigma 模型可能仍然具有消失的瞬子超势。