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<p>We propose to use the winding number of the gradient of a scalar potential as a simple topological index that relates critical points in the interior of the scalar field space to the behavior of the potential at the (asymptotic) boundary of the field space. We demonstrate this technique for supersymmetric flux compactifications of M-theory on Calabi-Yau four-folds, and use the Fermat sextic as a simple, one-parameter example.</p>

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An index for flux vacua

  • 期刊论文

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  • 发表日期：

    2026年1月21日

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  • Severin Lüst

摘要

We propose to use the winding number of the gradient of a scalar potential as a simple topological index that relates critical points in the interior of the scalar field space to the behavior of the potential at the (asymptotic) boundary of the field space. We demonstrate this technique for supersymmetric flux compactifications of M-theory on Calabi-Yau four-folds, and use the Fermat sextic as a simple, one-parameter example.