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arXiv 1702.08158hep-th
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爱因斯坦-杨-米尔斯振幅的展开

Expansion of Einstein-Yang-Mills Amplitude

Chih-Hao Fu, Yi-Jian Du, Rijun Huang, Bo Feng

摘要:

本文从不同的角度对单道Einstein-Yang-Mills振幅展开为色序Yang-Mills振幅的线性组合进行了深入的研究。利用规范不变性原理,我们提出了一个递归构造,其中任意数目引力子的EYM振幅可以展开为较少数目引力子的EYM振幅。通过这种构造,我们可以写出EYM振幅在色序Yang-Mills振幅基础上的完全展开式。作为副产品,我们能够写出BCJ分子的多项式形式,即,分子满足颜色运动学的对偶性,杨米尔斯振幅。在讨论了规范不变性之后,我们转向BCFW在壳递归关系,并讨论如何从在壳图像理解膨胀。最后给出了如何从KLT关系的角度解释展开式以及如何有效地求出展开式系数。

英文摘要:

In this paper, we provide a thorough study on the expansion of single trace Einstein-Yang-Mills amplitudes into linear combination of color-ordered Yang-Mills amplitudes, from various different perspectives. Using the gauge invariance principle, we propose a recursive construction, where EYM amplitude with any number of gravitons could be expanded into EYM amplitudes with less number of gravitons. Through this construction, we can write down the complete expansion of EYM amplitude in the basis of color-ordered Yang-Mills amplitudes. As a byproduct, we are able to write down the polynomial form of BCJ numerator, i.e., numerators satisfying the color-kinematic duality, for Yang-Mills amplitude. After the discussion of gauge invariance, we move to the BCFW on-shell recursion relation and discuss how the expansion can be understood from the on-shell picture. Finally, we show how to interpret the expansion from the aspect of KLT relation and the way of evaluating the expansion coefficients efficiently.

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