Skyrmions, Rational Maps & Scaling Identities

TL;DR

This paper improves approximate Skyrmion solutions derived from the rational map ansatz by applying scaling arguments, which helps clarify their true shape, whether more oblate or prolate, despite small energy improvements.

Contribution

It introduces a scaling-based method to refine Skyrmion solutions and analyze their shape characteristics beyond the initial rational map approximation.

Findings

Small energy improvements from scaling adjustments

Clarification of Skyrmion shapes as oblate or prolate

Enhanced understanding of Skyrmion geometry

Abstract

Starting from approximate Skyrmion solutions obtained using the rational map ansatz, improved approximate Skyrmions are constructed using scaling arguments. Although the energy improvement is small, the change of shape clarifies whether the true Skyrmions are more oblate or prolate.