Multisolitons 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 nonlinear sigma model without the need for a term that is quartic on derivatives of the pion fields (Skyrme term). The resulting model has proven to share many of the features that the usual Skyrme theory has, but with a better mathematical formulation in terms of the well posedness of its evolution equations. In the present work, we have numerically searched for static multisolitonic 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 in the Lagrangian and explored the low- and high-density phases of solitons for different ranges of the parameter space, achieving solitons localized enough, which allows for a comparison with planar (two-dimensional) studies.