A bstractIn this paper, we derive generalized Bern-Carrasco-Johansson (BCJ) relations for color-ordered Yang-Mills amplitudes by imposing gauge invariance conditions and dimensional reduction appropriately on the new discovered graphic expansion of Einstein-Yang-Mills amplitudes. These relations are also satisfied by color-ordered amplitudes in other theories such as bi-scalar theory and nonlinear sigma model (NLSM). As an application of the gauge invariance induced relations, we further prove that the three types of BCJ numerators in NLSM, which are derived from Feynman rules, Abelian Z-theory and Cachazo-He-Yuan (CHY) formula respectively, produce the same total amplitudes. In other words, the three distinct approaches to NLSM amplitudes are equivalent to each other.

中文翻译：

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规范不变性引起的关系和 NLSM 振幅不同方法之间的等价性

摘要在本文中，我们通过对新发现的爱因斯坦-杨-米尔斯振幅的图形展开适当地施加规范不变性条件和降维，推导出了颜色排序杨-米尔斯振幅的广义 Bern-Carrasco-Johansson (BCJ) 关系。这些关系也可以通过其他理论中的颜色排序幅度来满足，例如双标量理论和非线性西格玛模型 (NLSM)。作为规范不变性诱导关系的应用，我们进一步证明了NLSM中分别由Feynman规则、阿贝尔Z理论和Cachazo-He-Yuan(CHY)公式导出的三种BCJ分子产生相同的总数幅度。换句话说，NLSM 幅度的三种不同方法彼此等效。