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A curious correspondence has been known between Landau models and non-linearsigma models: Reinterpreting the base-manifolds of Landau models asfield-manifolds, the Landau models are transformed to non-linear sigma modelswith same global and local symmetries. With the idea of the dimensionalhierarchy of higher dimensional Landau models, we exploit this correspondenceto present a systematic procedure for construction of non-linear sigma modelsin higher dimensions. We explicitly derive $O(2k+1)$ non-linear sigma models in$2k$ dimension based on the parent tensor gauge theories that originate fromnon-Abelian monopoles. The obtained non-linear sigma models turn out to beSkyrme-type non-linear sigma models with $O(2k)$ local symmetry. Through adimensional reduction of Chern-Simons tensor field theories, we also deriveSkyrme-type $O(2k)$ non-linear sigma models in $2k-1$ dimension, which realizethe original and other Skyrme models as their special cases. As a unifieddescription, we explore Skyrme-type $O(d+1)$ non-linear sigma models andclarify their basic properties, such as stability of soliton configurations,scale invariant solutions, and field configurations with higher winding number.

A Unified Construction of Skyrme-type Non-linear sigma Models via The Higher Dimensional Landau Models