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<p>We study the cohomology of an elliptic differential complex arising from the infinitesimal moduli of heterotic string theory in the supergravity approximation. We compute these cohomology groups at the standard embedding, and show that they decompose into a direct sum of cohomologies. While this is often assumed in the literature, it had not been explicitly demonstrated. Given a stable gauge bundle over a complex threefold with trivial canonical bundle and no holomorphic vector fields, we also show that the Euler characteristic of this differential complex is zero. This points towards a perfect obstruction theory for the heterotic moduli problem, at least for the most physically relevant compactifications.</p>

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The decoupling of moduli about the standard embedding

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年1月2日

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  • Beatrice Chisamanga,
  • Jock McOrist,
  • Sebastien Picard,
  • Eirik Eik Svanes

摘要

We study the cohomology of an elliptic differential complex arising from the infinitesimal moduli of heterotic string theory in the supergravity approximation. We compute these cohomology groups at the standard embedding, and show that they decompose into a direct sum of cohomologies. While this is often assumed in the literature, it had not been explicitly demonstrated. Given a stable gauge bundle over a complex threefold with trivial canonical bundle and no holomorphic vector fields, we also show that the Euler characteristic of this differential complex is zero. This points towards a perfect obstruction theory for the heterotic moduli problem, at least for the most physically relevant compactifications.