Vector Bundle Moduli Superpotentials in Heterotic Superstrings and M-Theory
Vector Bundle Moduli Superpotentials in Heterotic Superstrings and M-Theory
复制标题
异质超弦和 M 理论中的向量丛模超势
DOI：
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发表时间：
2002
期刊：
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通讯作者：
B. Ovrut
中科院分区：
文献类型：
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作者：
E. Buchbinder;R. Donagi;B. Ovrut
由杂化超弦围绕属零全纯曲线缠绕一次所生成的非微扰超势与涉及该曲线上狄拉克算子行列式的普法夫成正比。我们证明该狄拉克算子的零模空间是依赖于相关向量丛模的线性映射的核心。通过显式计算该映射的行列式，我们可以推断出零模态空间的维数是否消失。结果表明，该信息足以完全确定普法夫式，从而确定非微扰超势作为向量丛模的显式全纯函数。通过许多重要的例子来说明该方法。
The non-perturbative superpotential generated by a heterotic superstring wrapped once around a genus-zero holomorphic curve is proportional to the Pfaffian involving the determinant of a Dirac operator on this curve. We show that the space of zero modes of this Dirac operator is the kernel of a linear mapping that is dependent on the associated vector bundle moduli. By explicitly computing the determinant of this map, one can deduce whether or not the dimension of the space of zero modes vanishes. It is shown that this information is sufficient to completely determine the Pfaffian and, hence, the non-perturbative superpotential as explicit holomorphic functions of the vector bundle moduli. This method is illustrated by a number of non-trivial examples.