4D flat-space scattering amplitude/CFT3 correlator correspondence revisited

In this paper, we make connection between CFT$_3$ three point correlation function of conserved currents and 4D amplitude general spin massless gauge field explicit. We do so by taking flat space limit momentum CFT show how they reproduce amplitudes. then out a mismatch number independent structures in 3D correlator covariant vertex higher fields. This is contrast with expectation that counting 3d 4d should match. even more pronounced spinor helicity variables. also an interesting relation parity odd space. observation helps us to construct new strtucture which accounts for the mismatch. However mention extra structure can't be constructed hence persists. Story variable complicated discussed detail. further comment on variables AdS amplitudes light cone