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