On Yang--Mills instantons over multi-centered gravitational instantons

TL;DR

This paper explicitly constructs and analyzes Yang--Mills instantons on multi-centered gravitational instantons, revealing their actions, reducibility, and related monopole solutions, thus advancing understanding of gauge fields in complex gravitational backgrounds.

Contribution

It provides explicit calculations of Yang--Mills instantons on multi-centered gravitational instantons, including their actions, reducibility, and monopole solutions, which is a novel extension of prior work.

Findings

Calculated instanton actions on multi-centered gravitational instantons.

Identified reducible instanton solutions.

Derived explicit monopole solutions from instantons.

Abstract

In this paper we explicitly calculate the analogue of the 't Hooft SU(2) Yang--Mills instantons on Gibbons--Hawking multi-centered gravitational instantons which come in two parallel families: the multi-Eguchi--Hanson, or A_k ALE gravitational instantons and the multi-Taub--NUT, or A_k ALF gravitational instantons. We calculate their action and find the reducible ones. Following Kronheimer we also exploit the U(1) invariance of our solutions and study the corresponding explicit singular SU(2) magnetic monopole solutions on Euclidean three-space.