Conformally soft gluons are conserved currents of the Celestial Conformal Field Theory (CCFT) and generate a Kac-Moody algebra. We study celestial amplitudes of Yang-Mills theory, which are Mellin transforms of gluon amplitudes and take the double soft limit of a pair of gluons. In this manner we construct the Sugawara energy-momentum tensor of the CCFT. We verify that conformally soft gauge bosons are Virasoro primaries of the CCFT under the Sugawara energy-momentum tensor. The Sugawara tensor though does not generate the correct conformal transformations for hard states. In Einstein-Yang- Mills (EYM) theory, we consider an alternative construction of the energy-momentum tensor, similar to the double copy construction which relates gauge theory amplitudes with gravity ones. This energy momentum tensor has the correct properties to generate conformal transformations for both soft and hard states. We extend this construction to supertranslations.

中文翻译：

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论天球上的菅原构造

共形软胶子是天体共形场理论 (CCFT) 的守恒电流，并生成 Kac-Moody 代数。我们研究杨米尔斯理论的天体振幅，这是胶子振幅的梅林变换，并采用一对胶子的双软极限。通过这种方式，我们构建了 CCFT 的 Sugawara 能量-动量张量。我们验证了共形软规范玻色子是菅原能量动量张量下 CCFT 的 Virasoro 主色。然而，菅原张量不会为硬态生成正确的共形变换。在爱因斯坦-杨-米尔斯 (EYM) 理论中，我们考虑了能量-动量张量的另一种构造，类似于将规范理论振幅与重力振幅相关联的双重复制构造。这种能量动量张量具有正确的属性，可以为软态和硬态生成共形变换。我们将这种结构扩展到超级翻译。