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