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

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

2006-10-02

arxiv.org/abs/hep-th/0610024v1

J.Phys.A40:1907,2007

Physics

High Energy Physics

High Energy Physics - Theory

23 pages

Scientific paper

10.1088/1751-8113/40/8/015

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.

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