Classification of normal modes for multiskyrmions

The normal mode spectra of multiskyrmions play a key role in their quantisation. We present a general method capable of predicting all 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.