New Integrable Sectors in Skyrme and 4-dimensional CP^n Model

TL;DR

This paper introduces new integrable sectors in Skyrme and $CP^n$ models in four dimensions, expanding the understanding of soliton solutions and integrability conditions in these nonlinear field theories.

Contribution

It derives a new integrable subsystem of the Skyrme model that includes non-holomorphic solutions and constructs a family of chiral Lagrangians with exact Skyrme-like solitons.

Findings

A new integrable subsystem of the Skyrme model is established.

A family of chiral Lagrangians with finite energy solitons is constructed.

A tower of integrable subsystems in $CP^n$ models is obtained.

Abstract

The application of a weak integrability concept to the Skyrme and $CP^n$ models in 4 dimensions is investigated. A new integrable subsystem of the Skyrme model, allowing also for non-holomorphic solutions, is derived. This procedure can be applied to the massive Skyrme model, as well. Moreover, an example of a family of chiral Lagrangians providing exact, finite energy Skyrme-like solitons with arbitrary value of the topological charge, is given. In the case of $CP^n$ models a tower of integrable subsystems is obtained. In particular, in (2+1) dimensions a one-to-one correspondence between the standard integrable submodel and the BPS sector is proved. Additionally, it is shown that weak integrable submodels allow also for non-BPS solutions. Geometric as well as algebraic interpretations of the integrability conditions are also given.