Baby Skyrmions on the Two-Sphere

TL;DR

This paper numerically finds static multi-soliton solutions of the baby Skyrme model on a two-sphere, revealing geometric structures and symmetries for charges up to 14, and connecting these to the 3D Skyrme model.

Contribution

It provides new numerical solutions for baby Skyrmions on a two-sphere and demonstrates the effectiveness of a rational map ansatz for approximations.

Findings

Charge-one Skyrmion is spherical

Charge-two Skyrmion is toroidal

Higher charge Skyrmions have discrete symmetries

Abstract

We find the static multi-soliton solutions of the baby Skyrme model on the two-sphere for topological charges 1 =< B =< 14. Numerical full-field results show that the charge-one Skyrmion is spherical, the charge-two Skyrmion is toroidal, and Skyrmions with higher charge all have point symmetries which are subgroups of O(3). We find that a rational map ansatz yields very good approximations to the full-field solutions. We point out a strong connection between the discrete symmetries of our solutions and those of corresponding solutions of the 3D Skyrme model.