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 Poincaré disc. The position of the skyrmion depends on the Taub–NUT mass parameter, and its topological charge is equal to two.