Multi-solitons with vector mesons on the two-sphere

Abstract

Recent studies have suggested a strong connection between the static solutions of the 3D Skyrme model and those corresponding to its low-dimensional analog (baby-Skyrme model) on a two-sphere. We have found almost identical solutions considering an alternative two-dimensional model in which a vector meson field is introduced and coupled to the system, instead of the usual Skyrme term. It has been known that including this vector meson field in three dimensions stabilizes the non-linear sigma model without the need of a term quartic on derivatives of the pion fields (Skyrme term). In the present work, we have numerically searched for static multi-solitonic solutions of this alternative stabilization, for the case in which the base-space is a two-sphere. Moreover, we analyze the stability of these solutions under small perturbations in a fully dynamical setting. We have also considered the inclusion of a particular potential term into the Lagrangian, and explored the low/high-density phases of solitons for different ranges of the parameter space, achieving solitons localized enough that allow us to compare with planar (two-dimensional) studies.