Factorization of Mellin amplitudes

TL;DR

This paper develops Mellin amplitudes for scalar and spinning operators in conformal field theories, revealing factorization properties and connecting them to flat space scattering amplitudes via the AdS/CFT correspondence.

Contribution

It introduces a general framework for Mellin amplitudes in CFTs with spin and establishes their relation to flat space scattering amplitudes, extending previous scalar-only results.

Findings

Mellin amplitudes have simple pole structures with factorized residues.

The flat space limit relates CFT Mellin amplitudes to bulk scattering amplitudes.

Generalization to operators with spin broadens the applicability of Mellin amplitude techniques.

Abstract

We introduce Mellin amplitudes for correlation functions of $k$ scalar operators and one operator with spin in conformal field theories (CFT) in general dimension. We show that Mellin amplitudes for scalar operators have simple poles with residues that factorize in terms of lower point Mellin amplitudes, similarly to what happens for scattering amplitudes in flat space. Finally, we study the flat space limit of Anti-de Sitter (AdS) space, in the context of the AdS/CFT correspondence, and generalize a formula relating CFT Mellin amplitudes to scattering amplitudes of the bulk theory, including particles with spin.