Towards Spinning Mellin Amplitudes

TL;DR

This paper develops a Mellin representation framework for four-point conformal correlators involving operators with arbitrary integer spins, introducing spinning Mellin amplitudes and a basis for computing them.

Contribution

It generalizes the Mellin transform to include spinning operators and proposes a new basis for calculating spinning Mellin amplitudes in conformal field theories.

Findings

Constructed Mellin representation for four-point functions with arbitrary spins.

Introduced discrete Mellin variables for spin degrees of freedom.

Generalized Mack polynomial for spinning Mellin amplitudes.

Abstract

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.