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 resummation 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 Bern-Dixon-Smirnov (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.

• Received 16 October 2020
• Accepted 25 November 2020

DOI:https://doi.org/10.1103/PhysRevD.102.126027

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Published by the American Physical Society