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Loops on the Celestial Sphere
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Loops on the Celestial Sphere
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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.
Forward citations
Cited by 5 Pith papers
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Topics in Celestial holography: A bottom-up perspective
A review of symmetries, celestial CFT, twistor theory interplay, and AdS/CFT connections in the bottom-up search for a celestial dual to flat-space quantum gravity.
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