Towards Spinning Mellin Amplitudes

We construct the Mellin representation of four point conformal correlation function with external primary operators with arbitrary integer spacetime spins, and obtain a natural proposal for spinning Mellin amplitudes. By restricting to the exchange of symmetric traceless primaries, we generalize the Mellin transform for scalar case to introduce discrete Mellin variables for incorporating spin degrees of freedom. Based on the structures about spinning three and four point Witten diagrams, we also obtain a generalization of the Mack polynomial which can be regarded as a natural kinematical polynomial basis for computing spinning Mellin amplitudes using different choices of interaction vertices.