Sphalerons in the Skyrme model

TL;DR

This paper uses numerical methods to find sphaleron solutions in the Skyrme model, revealing unstable configurations with zero topological charge that resemble Hopf solitons and depend on the charge number n.

Contribution

It introduces the first numerical computation of sphalerons in the Skyrme model, detailing their structure and stability properties for various topological charges.

Findings

Sphalerons have axial symmetry with zero topological charge.

Energy of sphalerons is slightly less than twice that of charge n Skyrmions.

For n > 4, Skyrmion and antiSkyrmion merge into a circle.

Abstract

Numerical methods are used to compute sphaleron solutions of the Skyrme model. These solutions have topological charge zero and are axially symmetric, consisting of an axial charge n Skyrmion and an axial charge -n antiSkyrmion (with n greater than one), balanced in unstable equilibrium. The energy is slightly less than twice the energy of the axially symmetric charge n Skyrmion. A similar configuration with n=1 does not produce a sphaleron solution, and this difference is explained by considering the interaction of asymptotic pion dipole fields. For sphaleron solutions with n greater than four the positions of the Skyrmion and antiSkyrmion merge to form a circle, rather than isolated points, and there are some features in common with Hopf solitons of the Skyrme-Faddeev model.