论文标题
平面空间上的Instantons：显式结构
Instantons on flat space: Explicit constructions
论文作者
论文摘要
在本说明中，我们重新审视了最初在物理学文献中最初发现的平面空间上激体子的一些著名示例。特别是，我们解释了$ \ mathbb {r}^4 $上的基本intsanton如何具有平坦的hyperkaehler结构，对$ \ mathbb {r}^7 $和$ \ mathbb {r}^8 $的自然概括分别为flat $ g_2 $ - 和spin（7）-manifolds。在Quaternionic几何学的意义上，我们还提供了$ \ Mathbb {H}^n $上ASD Instantons的鲜明构建的细节。
In this note, we revisit some well-known examples of instantons on flat space that were originally discovered in the physics literature. In particular, we explain how the basic instanton on $\mathbb{R}^4$, with its flat hyperkaehler structure, has natural generalisations to $\mathbb{R}^7$ and $\mathbb{R}^8$ viewed as flat $G_2$- and Spin(7)-manifolds, respectively. We also provide the details of an arguably less known construction of ASD instantons on $\mathbb{H}^n$, in the sense of quaternionic geometry.
