Skyrmion Vibration Modes within the Rational Map Ansatz

TL;DR

This paper investigates the vibration modes of Skyrmions using the rational map ansatz, revealing decoupled radial and map vibrations and comparing analytical results with numerical data for different baryon numbers.

Contribution

It introduces an analytical approach to study Skyrmion vibrations within the rational map framework, providing insights into mode decoupling and frequency comparisons.

Findings

Decoupling of radial and map vibrations

Qualitative agreement with numerical vibration modes

Discrepancies in vibration frequencies

Abstract

We study the vibration modes of the Skyrme model within the rational map ansatz. We show that the vibrations of the radial profiles and the rational maps are decoupled and we consider explicitly the case B=1, B=2 and B=4. We then compare our results with the vibration modes obtained numerically by Barnes et al. and show that qualitatively the rational map reproduces the vibration modes obtained numerically but that the vibration frequencies of these modes do not match very well.