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arXiv 1707.02192hep-th
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$R^2$引力和$(DF)^2$规范理论的Ambitwistor公式

Ambitwistor formulations of $R^2$ gravity and $(DF)^2$ gauge theories

Thales Azevedo, Oluf Tang Engelund

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35 pages; v2: references added/updated, revised version
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摘要：

从CHY公式和Ambitwistor弦论的角度考虑$D$维振幅在$R^2$引力（$D=4$中的共形引力）和最近引入的$(DF)^2$规范理论中的作用。这些理论通过BCJ双拷贝结构联系起来，而$(DF)^2$规范理论服从色运动学对偶性。我们的工作，这些理论的世界表的细节，并表明，他们承认一个配方作为积分的散射方程的支持下，或者，作为ambitwistor弦论。对于引力，这将伯科维奇和威滕关于共形引力的工作推广到了$D$维。ambitwistor也被解释为Witten扭量弦（SYM +共形超引力）的$D$维推广。作为我们的ambitwistor调查的一部分，我们发现了另一个$(DF)^2$规范理论包含一个光子耦合到爱因斯坦引力。与通常的杨-米尔斯平方相比，这个理论可以提供爱因斯坦引力的另一种KLT描述。

英文摘要：

We consider $D$-dimensional amplitudes in $R^2$ gravities (conformal gravity in $D=4$) and in the recently introduced $(DF)^2$ gauge theory, from the perspective of the CHY formulae and ambitwistor string theory. These theories are related through the BCJ double-copy construction, and the $(DF)^2$ gauge theory obeys color-kinematics duality. We work out the worldsheet details of these theories and show that they admit a formulation as integrals on the support of the scattering equations, or alternatively, as ambitwistor string theories. For gravity, this generalizes the work done by Berkovits and Witten on conformal gravity to $D$ dimensions. The ambitwistor is also interpreted as a $D$-dimensional generalization of Witten's twistor string (SYM + conformal supergravity). As part of our ambitwistor investigation, we discover another $(DF)^2$ gauge theory containing a photon that couples to Einstein gravity. This theory can provide an alternative KLT description of Einstein gravity compared to the usual Yang-Mills squared.

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