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arXiv · hep-th/0610024

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

C. Adam·J. Sanchez-Guillen·A. Wereszczynski
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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.

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C. Adam, J. Sanchez-Guillen, A. Wereszczynski. 2006-10-02. New Integrable Sectors in Skyrme and 4-dimensional CP^n Model. https://doi.org/10.1088/1751-8113%2F40%2F8%2F015

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