Yang-Mills Instantons in the Gravitational Instanton Backgrounds

TL;DR

This paper introduces a new algorithm for generating (anti) self-dual Yang-Mills solutions in gravitational instanton backgrounds, producing exotic configurations with finite action and fractional topological charge.

Contribution

A novel algorithm for constructing Yang-Mills instantons in gravitational instanton backgrounds, applied to Taub-NUT and Eguchi-Hanson metrics, revealing exotic solutions.

Findings

Solutions have finite YM action

Solutions exhibit fractional topological charge

Applied successfully to Taub-NUT and Eguchi-Hanson metrics

Abstract

The simplest and the most straightforward new algorithm for generating solutions to (anti) self-dual Yang-Mills (YM) equation in the typical gravitational instanton backgrounds is proposed. When applied to the Taub-NUT and the Eguchi-Hanson metrics, the two best-known gravitational instantons, the solutions turn out to be the rather exotic type of instanton configurations carrying finite YM action but generally fractional topological charge values.