论文标题
旋转（7）Instantons和Hermitian Yang-Mills连接，用于Stenzel度量
Spin(7) Instantons and Hermitian Yang-Mills Connections for the Stenzel Metric
论文作者
论文摘要
我们在$ t^{\ star} s^{4} $上使用Stenzel渐近的锥形Calabi-yau度量的大型等轴测组来研究自旋（7）Instanton和Hermitian-Yang-Yang Mills（Hym）方程之间的关系。我们将这两个问题都减少到可容纳的ODE并寻找不变解决方案。在亚伯利亚案中，我们建立了当地的等效性，并证明了全球不存在的结果。我们通过结构组（3）分析了非亚伯方程，并在这种情况下构建了不变自旋（7）intstons的模量空间。这包括一个显式的一个不可约性自旋（7）的参数家族，其中之一是HYM。因此，我们负面解决了有关两个量规理论PDE的等效性的问题。 HYM连接在该模量空间的压缩中起作用，表现出我们旨在在未来工作中进一步研究的现象。
We use the large isometry group of the Stenzel asymptotically conical Calabi-Yau metric on $T^{\star}S^{4}$ to study 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 includes an explicit one parameter family of irreducible Spin(7) instantons only one of which is HYM. 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 a phenomenon that we aim to further look into in future work.
