Yang-Mills Instantons from Gravitational Instantons

TL;DR

This paper demonstrates that gravitational instantons can be viewed as SU(2) Yang-Mills instantons on Ricci-flat four-manifolds, establishing a direct correspondence between these two types of instantons and exploring their topological features.

Contribution

It establishes that all gravitational instantons are equivalent to SU(2) Yang-Mills instantons on Ricci-flat manifolds, providing explicit examples and analyzing their topological properties.

Findings

Gravitational instantons satisfy the same self-duality equations as SU(2) Yang-Mills instantons.

A correspondence between gravitational and Yang-Mills instantons is explicitly demonstrated.

Topological properties of these instantons are discussed and exemplified.

Abstract

We show that every gravitational instantons are SU(2) Yang-Mills instantons on a Ricci-flat four manifold although the reverse is not necessarily true. It is shown that gravitational instantons satisfy exactly the same self-duality equation of SU(2) Yang-Mills instantons on the Ricci-flat manifold determined by the gravitational instantons themselves. We explicitly check the correspondence with several examples and discuss their topological properties.