Pullback of the Volume Form, Integrable Models in Higher Dimensions and Exotic Textures

Abstract

A procedure allowing for the construction of Lorentz invariant integrable models living in d+1 dimensional space-time and with an n dimensional target space is provided. Here, integrability is understood as the existence of the generalized zero-curvature formulation and infinitely many conserved quantities. A close relation between the Lagrange density of the integrable models and the pullback of the pertinent volume form on target space is established. Moreover, we show that the conserved currents are Noether currents generated by the volume preserving diffeomorphisms. Further, we show how such models may emerge via abelian projection of some gauge theories. Then we apply this framework to the construction of integrable models with exotic textures. Particularly, we consider integrable models providing exact suspended Hopf maps i.e., solitons with a nontrivial topological charge of pi_4(S^3). Finally, some families of integrable models with solitons of pi_n(S^n) type are constructed. Infinitely many exact solutions with arbitrary value of the topological index are found. In addition, we demonstrate that they saturate a Bogomolny bound.

23 pages

References in corpus (8)

• Investigation of the Nicole model
• New Integrable Sectors in Skyrme and 4-dimensional CP^n Model
• Conservation laws in Skyrme-type models
• Exact time dependent Hopf solitons in 3+1 dimensions
• Localized Gravity on Topological Abelian Higgs Strings
• Goldstone models in D+1 dimensions, D=3,4,5, supporting stable and zero topological charge solutions
• Noncommutative Nonlinear Sigma Models and Integrability
• Integrable subsystem of Yang--Mills dilaton theory

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• On DBI Textures with Generalized Hopf Fibration
• Characteristic analysis for integrable soliton models on two-dimensional target spaces
• Radial Stabilization of Magnetic Skyrmions Under Strong External Magnetic Field