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

TL;DR

This paper derives explicit multi-instanton solutions to the selfdual Yang-Mills equations on various curved spaces with $SO(3)$ symmetry, extending known solutions from flat space to curved backgrounds.

Contribution

It provides the first explicit multi-instanton solutions on curved spaces with $SO(3)$ isometry, generalizing previous flat space results.

Findings

Exact multi-instanton solutions on curved spaces like Einstein static universe and $ ext{R} imes$ dS$_3^E$

Solutions exhibit explicit multi-centered and topological properties

Existence of solutions confirmed on multiple curved backgrounds

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.