Spin(7) Instantons and Hermitian Yang–Mills Connections for the Stenzel Metric
Spin(7) Instantons and Hermitian Yang–Mills Connections for the Stenzel Metric
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Stenzel 度量的自旋 (7) 瞬子和 Hermitian Yang-Mills 连接
DOI：
10.1007/s00220-021-04055-5
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发表时间：
2020
影响因子：
2.4
通讯作者：
Vasileios Ektor Papoulias
中科院分区：
文献类型：
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作者：
Vasileios Ektor Papoulias
我们用高度对称的Stenzel Calabi-Yau结构作为检验Spin（7）瞬子和Hermitian-Yang-米尔斯（HYM）方程之间关系的基础。我们减少这两个问题，易于处理的常微分方程，并寻找不变的解决方案。在阿贝尔情形下，我们建立了局部等价，并证明了一个全局不存在的结果。我们分析了具有SO（3）结构群的非交换方程，并在此基础上构造了不变Spin（7）瞬子的模空间。这是由两个1-参数家族组成的-其中一个是显式的-不可约自旋（7）瞬子。每个都有一个独特的HYM连接。这样，我们就否定地解决了关于两个规范论偏微分方程等价性的问题。HYM连接在这个模空间的紧化中发挥作用，表现出可移动的奇异现象，我们的目标是在未来的工作中进一步研究。
We use the highly symmetric Stenzel Calabi–Yau structure onas a testing ground for the relationship between the Spin(7) instanton and Hermitian–Yang–Mills (HYM) equations. We reduce both problems to tractable ODEs and look for invariant solutions. In the abelian case, we establish local equivalence and prove a global nonexistence result. We analyze the nonabelian equations with structure group SO(3) and construct the moduli space of invariant Spin(7) instantons in this setting. This is comprised of two 1-parameter families—one of them explicit—of irreducible Spin(7) instantons. Each carries a unique HYM connection. We thus negatively resolve the question regarding the equivalence of the two gauge theoretic PDEs. The HYM connections play a role in the compactification of this moduli space, exhibiting aremovable singularityphenomenon that we aim to further examine in future work.