Instantons on flat space: Explicit constructions

Abstract

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.

13 pages