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In this paper, we make connection between CFT$_3$ three point correlationfunction of conserved currents and 4D three point amplitude of general spinmassless gauge field explicit. We do so by taking flat space limit of momentumspace CFT correlation function and show how they reproduce flat spaceamplitudes. We then point out a mismatch between number of independentstructures in 3D CFT correlator of conserved currents and 4D flat spacecovariant vertex of massless higher spin fields. This is in contrast withgeneral expectation that counting of 3d CFT correlator and 4d flat spaceamplitude should match. This mismatch is even more pronounced in spinorhelicity variables. We also point out an interesting relation between parityeven and parity odd flat space amplitude in momentum space. This observationhelps us to construct a new momentum space CFT strtucture which accounts forthe mismatch. However we should mention that this extra CFT structure can't beconstructed out of conserved currents and hence counting mismatch between CFTcorrelation of conserved currents and flat space amplitude of massless gaugefield persists. Story in spinor helicity variable is more complicated and isdiscussed in detail. We further comment on the connection of CFT correlationfunction in spinor helicity variables to AdS amplitudes in spinor helicityvariables and light cone variables.

4D Flat-space scattering amplitude /$CFT_3$ correlator correspondence revisited