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

TL;DR

This paper develops a systematic method to construct higher-dimensional Skyrme-type non-linear sigma models from Landau models, revealing their properties and connections to tensor gauge theories and monopoles.

Contribution

It introduces a unified construction framework for Skyrme-type models in various dimensions using higher-dimensional Landau models and tensor gauge theories.

Findings

Explicit derivation of $O(2k+1)$ sigma models in $2k$ dimensions.

Derivation of Skyrme-type $O(2k)$ models in $2k-1$ dimensions.

Analysis of soliton stability and higher winding solutions.

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.