On $d=4$ Yang-Mills instantons in a spherically symmetric background

TL;DR

This paper argues for the existence of self-dual Yang-Mills instantons in spherically symmetric Euclidean backgrounds, showing they have finite action and do not alter the geometry, and conjectures similar solutions exist broadly.

Contribution

It provides theoretical evidence for self-dual Yang-Mills instantons in spherically symmetric backgrounds and conjectures their general existence in nonextremal cases.

Findings

Existence of instantons with finite action and zero energy-momentum tensor.

Instantons do not disturb the background geometry.

Conjecture of similar solutions in general nonextremal backgrounds.

Abstract

We present arguments for the existence of self-dual Yang-Mills instantons for several spherically symmetric backgrounds with Euclidean signature. The time-independent Yang-Mills field has finite action and a vanishing energy momentum tensor and does not disturb the geometry. We conjecture the existence of similar solutions for any nonextremal SO(3)-spherically symmetric background.