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arXiv · 1803.01701

Gauge invariance induced relations and the equivalence between distinct approaches to NLSM amplitudes

Yi-Jian Du·Yong Zhang
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Abstract

In this paper, we derive generalized Bern-Carrasco-Johansson 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 color-scalar theory, 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 formula respectively, produce the same total amplitudes. In other words, the three distinct approaches to NLSM amplitudes are equivalent to each other.

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Yi-Jian Du, Yong Zhang. 2018-06-19. Gauge invariance induced relations and the equivalence between distinct approaches to NLSM amplitudes. https://doi.org/10.1007/jhep07(2018)177

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