Skyrmions from gravitational instantons
High Energy Physics - Theory
2017-02-08 v2 General Relativity and Quantum Cosmology
Mathematical Physics
Differential Geometry
math.MP
Exactly Solvable and Integrable Systems
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.
Keywords
Cite
@article{arxiv.1206.0016,
title = {Skyrmions from gravitational instantons},
author = {Maciej Dunajski},
journal= {arXiv preprint arXiv:1206.0016},
year = {2017}
}
Comments
Major changes: The Atiyah-Hitchin manifold and the corresponding skyrmion discussed in more detail, gauge fixing procedure clarified, earlier errors corrected. Final version, to appear in Proceedings of the Royal Society A