State-operator correspondence in celestial conformal field theory

The bulk-to-boundary dictionary for 4D celestial holography is given a new entry defining 2D boundary states living on oriented circles the sphere. are constructed using CFT state-operator correspondence from operator insertions corresponding to either incoming or outgoing particles which cross sphere inside circle. BPZ construction applied give an inner product such whose associated bulk adjoints shown involve shadow transform. Scattering amplitudes then by products between same circle but with opposite orientations. found encode information as their counterparts, organized in radically different manner.