Skyrmions from gravitational instantons

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.