A bstractIn this note, we investigate relations between tree-level off-shell currents in nonlinear sigma model. Under Cayley parametrization, all odd-point currents vanish. We propose and prove a generalized U(1) identity for even-point currents. The off-shell U(1) identity given in [1] is a special case of the generalized identity studied in this note. The on-shell limit of this identity is equivalent with the on-shell KK relation. Thus this relation provides the full off-shell correspondence of tree-level KK relation in nonlinear sigma model.

中文翻译：

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非线性 sigma 模型中壳外关系的注意事项

摘要在本笔记中，我们研究了非线性 sigma 模型中树级壳外电流之间的关系。在 Cayley 参数化下，所有奇数点电流都消失了。我们提出并证明了偶数点电流的广义 U(1) 恒等式。[1] 中给出的壳外 U(1) 恒等式是本笔记中研究的广义恒等式的一个特例。此身份的壳上限制等效于壳上 KK 关系。因此，这种关系提供了非线性 sigma 模型中树级 KK 关系的完整壳外对应关系。