Skyrmions and Bags in the 2D-O(3) model

Abstract

Localized static solutions of the 2D-O(3) model are investigated in a representation with the 3-vector field $\vec Phi$ split into the unit vector $\hat Phi$ and the modulus $Φ$. As in the nonlinear version of the model this allows for the definition of a topological winding number $B$, and for the separation of the complete configuration space into distinct $B$-sectors. For small values of the $Φ^4$-coupling strength the stable energy minima in these sectors are characterized by bag formation in the modulus field which in the standard cartesian representation of the linear O(3) model would be unstable towards decay into the trivial B=0 vacuum. Stabilized by $B$-conservation they exhibit a surprising variety of very appealing features for multiply charged systems. With the total charge bound into one common deep bag opposite ways of distributing the topological charge density inside the bag can be realized: Pointlike structures which retain the individuality of single constituents (or doubly charged pairs), or a deconfined charge density spread uniformly throughout the interior of the bag. It is suggested that this extension supplies a crucial link to overcome the unsatisfactory existing mismatch between multiskyrmion configurations and nuclear structure.