Skyrmions from gravitational instantons

TL;DR

This paper introduces a novel method to construct Skyrme fields using the holonomy of the spin connection in gravitational instantons, specifically applying it to Atiyah-Hitchin and Taub-NUT instantons.

Contribution

It presents a new geometric approach to generate Skyrme fields from gravitational instantons, with explicit examples and analysis of the resulting skyrmions.

Findings

Explicit skyrmion from Taub-NUT instanton with topological charge two

Skyrmion domain is a circle bundle over the Poincare disc

Skyrmion position varies with Taub-NUT mass parameter

Abstract

We propose a construction of Skyrme fields from holonomy of the spin connection of gravitational instantons. The procedure is implemented for Atiyah-Hitchin and Taub-NUT instantons. The skyrmion resulting from the Taub-NUT is given explicitly on the space of orbits of a left translation inside the whole isometry group. The domain of the Taub-NUT skyrmion is a trivial circle bundle over the Poincare disc. The position of the skyrmion depends on the Taub-NUT mass parameter, and its topological charge is equal to two.