Deformation of the CP(1) model leading to fixed size solitons in 2+1 dimensions

Abstract

We discuss static particle-like solitons in the (2+1)-dimensional CP(1) model with a small mass deformation m preserving a U(1) × Z2 symmetry in the Lagrangian. Due to the breaking of scale invariance, the energy function becomes a strictly increasing function of the soliton size ρ, and therefore no classical finite size solution exists in this model. To remedy this we employ a well known technique of introducing a fourth-order derivative term in the Lagrangian to force the soliton action to diverge at small values of ρ. With this additional term the action exhibits a stable minimum at fixed size ρ.