Skyrme model on S_3 and Harmonic maps

TL;DR

This paper introduces a non-linear sigma model on S_3 that emulates the Skyrme model, constructs classical solutions numerically, and explores their behavior at critical coupling values, linking to harmonic maps.

Contribution

It proposes a new sigma model on S_3, constructs classical solutions numerically, and connects these solutions to harmonic maps at zero coupling.

Findings

Solutions exhibit catastrophe-like spikes at critical coupling values.

At zero coupling, solutions match previously known harmonic maps.

Numerical methods successfully construct solutions to the model's equations.

Abstract

A non-linear sigma model mimicking the Skyrme model on S_3 is proposed and a family of classical solutions to the equations are constructed numerically. The solutions terminate into catastrophe-like spikes at critical values of the Skyrme coupling constant and, when this constant is zero, they coincide with the series of Harmonic maps on S_3 constructed some years ago by P. Bizon.