论文标题
循环天体
Loops on the Celestial Sphere
论文作者
论文摘要
我们研究了循环校正对零无穷大的天体球体的循环校正的影响。我们首先在纯阳米尔斯理论和爱因斯坦重力中分析有限的一环天体振幅。然后，我们转向我们的主要重点：红外发散环振幅$ \ MATHCAL {N} = 4 $ SUPER YANG-MILLS理论。我们在维数正则化中计算天体的一环振幅，并表明它可以作为作用于天体树水平振幅的操作员重塑。这延伸到任何循环顺序，所有平面环的重新点击使我们能够写下全环天体振幅的表达式。最后，我们表明，由BDS公式给出的凸起的全环表达在天体球上促进到作用在树级的共形相关函数上的操作员，从而产生了celestial bds公式。
We study the effect of loop corrections to conformal correlators on the celestial sphere at null infinity. We first analyze finite one-loop celestial amplitudes in pure Yang-Mills theory and Einstein gravity. We then turn to our main focus: infrared divergent loop amplitudes in planar $\mathcal{N}=4$ super Yang-Mills theory. We compute the celestial one-loop amplitude in dimensional regularization and show that it can be recast as an operator acting on the celestial tree-level amplitude. This extends to any loop order and the re-summation of all planar loops enables us to write down an expression for the all-loop celestial amplitude. Finally, we show that the exponentiated all-loop expression given by the BDS formula gets promoted on the celestial sphere to an operator acting on the tree-level conformal correlation function, thus yielding, the celestial BDS formula.
