Title: The decoupling of moduli about the standard embedding Show Chinese title

Title: 模量关于标准嵌入的解耦

Abstract: We study the cohomology of an elliptic differential complex arising from the infinitesimal moduli of heterotic string theory. 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. Show Chinese abstract

Abstract: 我们研究来自杂化弦理论的无穷小模空间的椭圆微分复形的上同调。 我们在标准嵌入下计算这些上同调群，并表明它们分解为上同调的直和。 虽然这在文献中通常被假设，但尚未明确证明。 给定一个复三维流形上的稳定规范丛，该流形具有平凡的典范层且没有全纯向量场，我们也证明了这个微分复形的欧拉示性数为零。 这指向了杂化弦模空间问题的一个完美障碍理论，至少对于最符合物理需求的紧化情况而言。