Hyperbolic Skyrmions

TL;DR

This paper explores SU(2) Skyrmions in hyperbolic space, analyzing their solutions, approximations, and dynamics, revealing how curvature influences minimal energy configurations and their relation to Euclidean models.

Contribution

It introduces numerical solutions for hyperbolic Skyrmions, links curvature to pion mass effects, and compares their properties and dynamics to Euclidean Skyrmions.

Findings

Increased curvature improves rational map approximation accuracy.

Crystal chunk configurations are minimal energy solutions at higher curvature.

Hyperbolic Skyrmion dynamics show both similarities and differences to Euclidean models.

Abstract

We investigate SU(2) Skyrmions in hyperbolic space, by computing numerical solutions of the nonlinear field equation. We first demonstrate the link between increasing curvature and the accuracy of the rational map approximation to the minimal energy static solutions. We investigate the link between Skyrmions with massive pions in Euclidean space and the massless case in hyperbolic space, by relating curvature to the pion mass. Crystal chunks are found to be the minimal energy solution for increased curvature as well as increased mass of the model. The dynamics of the hyperbolic model are also simulated, with the similarities and differences to the Euclidean model noted.