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.
Highlights
Non-linear sigma (NLS) models were originally introduced for a description of mesons in hadron physics around 1960 [1, 2, 3, 4, 5, 6]
The present SO(2k) local symmetry stems from the gauge symmetry of the particular form of the parent tensor field action, while the hidden SO(2k) local symmetry exists in any NLS models whose field-manifold is S2k
Exploiting the differential geometry of the Landau models, we introduced the [k/2] distinct parent tensor gauge theories on the field-manifold S2k and subsequently derived the [k/2] O(2k + 1) Skyrme-type non-linear sigma model (S-NLS) models on R2pkhys
Summary
Non-linear sigma (NLS) models were originally introduced for a description of mesons in hadron physics around 1960 [1, 2, 3, 4, 5, 6]. The Chern-Simons statistical field coupled to the O(3) NLS model solitons provides a field theoretical description of anyons [48, 49] and such anyons are realized as fractionally charge excitations of the fractional quantum Hall effect [50, 51]. Another important example is about their analogous mathematical structures.
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