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

TL;DR

This paper investigates how adding a higher-derivative term to the 2+1 dimensional CP(1) model stabilizes soliton size by breaking scale invariance, resulting in fixed-size, finite-energy solutions.

Contribution

It demonstrates that a fourth-order derivative term can stabilize soliton size in the CP(1) model, which normally lacks finite size solutions due to scale invariance breaking.

Findings

Introducing a fourth-order derivative term stabilizes soliton size.

The modified model admits stable, finite-size soliton solutions.

Scale invariance breaking leads to a size-dependent energy function.

Abstract

We discuss static particle-like solitons in the 2+1 dimensional CP(1) model with a small mass deformation $m$ preserving a $U(1) \times Z_2$ symmetry in the Lagrangian. Due to the breaking of scale invariance, the energy function becomes a strictly increasing function of the soliton size $\rho$, and therefore no classical finite size solution exists in this model. To remedy this we employ a well known technique of introducing a forth-order derivative term in the Lagrangian to force the soliton action to diverge at small values of $\rho$. With this additional term the action exhibits a stable minimum at fixed size $\rho$.