论文标题
Skyrme型非线性Sigma模型的统一结构通过较高的尺寸Landau模型
A Unified Construction of Skyrme-type Non-linear sigma Models via The Higher Dimensional Landau Models
论文作者
论文摘要
在Landau模型和非线性Sigma模型之间已经知道了一个奇怪的对应关系：将Landau模型的基本模型重新诠释为现场模型，Landau模型被转换为具有相同全局和局部对称性的非线性Sigma模型。借助高维兰道模型的尺寸层次结构的想法，我们利用了此对应关系，以提出一个系统的程序，用于在较高维度中构建非线性Sigma模型。我们明确地基于$ 2K $ dimension $ O（2K+1）$非线性Sigma型号，该尺寸基于源自非阿布莱尼单极管的母体张量表理论。获得的非线性Sigma模型原来是具有$ O（2K）$本地对称性的Skyrme型非线性Sigma模型。通过减少Chern-Simons Tensor Field理论的尺寸，我们还以$ 2K-1 $ dimension的形式得出了Skyrme型$ O（2K）$非线性Sigma型号，这将原始和其他Skyrme模型视为其特殊情况。作为一个统一的描述，我们探索了Skyrme型$ O（D+1）$非线性Sigma模型并阐明其基本属性，例如孤子配置的稳定性，比例不变的解决方案和具有较高绕组数的现场配置。
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.
