A conformal map identifies the flat-space soft gluon S-algebra with light-ray operators built from CFT3 currents and their descendants in AdS4.
The self-dual sector of QCD amplitudes
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abstract
We provide an action for self-dual Yang-Mills theory which is a simple truncation of the usual Yang-Mills action. Only vertices that violate helicity conservation maximally are included. One-loop amplitudes in the self-dual theory then follow as a subset of the Yang-Mills ones. In light-cone gauges this action is almost identical to previously proposed actions, but in this formulation the vanishing of all higher-loop amplitudes is obvious; the explicit perturbative S-matrix is known. Similar results apply to gravity.
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All self-dual theories with or without higher-spin fields possess nontrivial tree-level amplitudes in Kleinian or complex Minkowski kinematics, completing the celestial analogue of the higher-spin duality.
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Soft Algebras in AdS$_4$ from Light Ray Operators in CFT$_3$
A conformal map identifies the flat-space soft gluon S-algebra with light-ray operators built from CFT3 currents and their descendants in AdS4.
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Amplitudes in self-dual (higher-spin) theories
All self-dual theories with or without higher-spin fields possess nontrivial tree-level amplitudes in Kleinian or complex Minkowski kinematics, completing the celestial analogue of the higher-spin duality.