Spontaneous Breaking of Rotational Symmetry in Rotating Solitons - a Toy Model of Excited Nucleons with High Angular Momentum

We study the phenomenon of spontaneous breaking of rotational symmetry (SBRS) in the rotating solutions of two types of baby Skyrme models. In the first the domain is a two-sphere and in the other, the Skyrmions are confined to the interior of a unit disk. Numerical full-field results show that when the angular momentum of the Skyrmions increases above a certain critical value, the rotational symmetry of the solutions is broken and the minimal energy configurations become less symmetric. We propose a possible mechanism as to why SBRS is present in the rotating solutions of these models, while it is not observed in the `usual' baby Skyrme model. Our results might be relevant for a qualitative understanding of the non-spherical deformation of excited nucleons with high orbital angular momentum.