Exact Multi-Instanton Solutions to Selfdual Yang-Mills Equation on Curved Spaces

Abstract

We find exact multi-instanton solutions to the selfdual Yang-Mills equation on a large class of curved spaces with $SO(3)$ isometry, generalizing the results previously found on ${\mathbb{R}}^4$. The solutions are featured with explicit multi-centered expressions and topological properties. As examples, we demonstrate the approach on several different curved spaces, including the Einstein static universe and $\mathbb{R}\times$ dS${}_3^E$, and show that the exact multi-instanton solutions exist on these curved backgrounds.

Comments: 6 pages, 4 figures; V2: published version, more discussions added