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arXiv 1208.0876hep-th
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高维算子振幅的色运动学对偶和双拷贝构造

Color-kinematics duality and double-copy construction for amplitudes from higher-dimension operators

Johannes Broedel, Lance J. Dixon

备注：
v2: published version, corrected eqns. (3.37) and (3.39). v1: 47 pages, 3 figures
发表信息：
JHEP 2010 (2012) 091
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摘要：

我们调查的颜色运动学对偶规范理论振幅产生的纯非阿贝尔杨米尔斯行动变形的高维运营商。对于用F^3表示的算符，即三个场强的乘积，色-运动学对偶表象的存在性是由弦论单值关系得出的。我们提供了明确的对偶表示，并显示如何基于它们的重力振幅的双副本建设是一致的Kawai-Lewellen-Tye关系。它导致了爱因斯坦引力与介子场耦合产生的振幅，并被形式为φ R^2和R^3的算符变形。对于维数比F^3更高的算子，例如在玻色子和超弦理论的低能展开中出现在下一阶的F^4型算子，情况更加复杂。某些F^4算子的颜色结构与基于结构常数f^{abc}的简单颜色-运动学对偶不相容，但即使是颜色相容的F^4算子也不承认对偶性。相比之下，超弦有效作用量的α素数展开式中的下一项--D^2、F^4和F^5型算符的特殊线性组合--确实承认对偶性，至少对于多达6个外部胶子的振幅是这样。

英文摘要：

We investigate color-kinematics duality for gauge-theory amplitudes produced by the pure nonabelian Yang-Mills action deformed by higher-dimension operators. For the operator denoted by F^3, the product of three field strengths, the existence of color-kinematic dual representations follows from string-theory monodromy relations. We provide explicit dual representations, and show how the double-copy construction of gravity amplitudes based on them is consistent with the Kawai-Lewellen-Tye relations. It leads to the amplitudes produced by Einstein gravity coupled to a dilaton field phi, and deformed by operators of the form phi R^2 and R^3. For operators with higher dimensions than F^3, such as F^4-type operators appearing at the next order in the low-energy expansion of bosonic and superstring theory, the situation is more complex. The color structure of some of the F^4 operators is incompatible with a simple color-kinematics duality based on structure constants f^{abc}, but even the color-compatible F^4 operators do not admit the duality. In contrast, the next term in the alpha-prime expansion of the superstring effective action --- a particular linear combination of D^2 F^4 and F^5-type operators --- does admit the duality, at least for amplitudes with up to six external gluons.

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