Multisolitons with vector mesons on the two-sphere

Abstract

Recent studies have suggested a strong connection between the static solutions of the 3D Skyrme modeland those corresponding to its low-dimensional analog (baby-Skyrme model) on a two-sphere. We havefound almost identical solutions considering an alternative two-dimensional model in which a vector mesonfield is introduced and coupled to the system, instead of the usual Skyrme term. It has been known thatincluding this vector meson field in three dimensions stabilizes the nonlinear sigma model without the needfor a term that is quartic on derivatives of the pion fields (Skyrme term). The resulting model has proven toshare many of the features that the usual Skyrme theory has, but with a better mathematical formulation interms of the well posedness of its evolution equations. In the present work, we have numerically searchedfor static multisolitonic solutions of this alternative stabilization, for the case in which the base space is atwo-sphere. Moreover, we analyze the stability of these solutions under small perturbations in a fullydynamical setting. We have also considered the inclusion of a particular potential term in the Lagrangianand 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.