Classification of Normal Modes for Multiskyrmions

TL;DR

This paper introduces a method to predict and classify low-lying vibrational modes of multiskyrmions, revealing complex mode structures and suggesting a richer moduli space for N>3.

Contribution

A general method for predicting and classifying vibrational modes of multiskyrmions, explaining higher multipole breathing modes, and proposing a more complex moduli space structure.

Findings

Classified vibrational modes by symmetry group

Explained origin of higher multipole breathing modes

Indicated a richer moduli space for N>3

Abstract

The normal mode spectra of multiskyrmions play a key role in their quantisation. We present a general method capable of predicting all the low-lying vibrational modes of known minimal energy multiskyrmions. In particular, we explain the origin of the higher multipole breathing modes, previously observed but not understood. We show how these modes may be classified according to the symmetry group of the static solution. Our results provide strong hints that the N-skyrmion moduli space, for N>3, may have a richer structure than previously thought, incorporating 8N-4 degrees of freedom.