Mellin Amplitudes for Fermionic Conformal Correlators

TL;DR

This paper develops Mellin amplitudes for fermionic conformal correlators, revealing their structure and pole behavior, with explicit examples in three dimensions and for tree-level diagrams involving fermions.

Contribution

It introduces a new formulation of Mellin amplitudes for fermionic correlators, including their tensor components and pole structures, expanding the tools for conformal field theory analysis.

Findings

Mellin amplitudes for fermionic correlators are explicitly constructed.

Each component of the Mellin amplitude can have multiple pole series.

Explicit examples demonstrate the properties of these amplitudes in specific cases.

Abstract

We define Mellin amplitudes for the fermion-scalar four point function and the fermion four point function. The Mellin amplitude thus defined has multiple components each associated with a tensor structure. In the case of three spacetime dimensions, we explicitly show that each component factorizes on dynamical poles onto components of the Mellin amplitudes for the corresponding three point functions. The novelty here is that for a given exchanged primary, each component of the Mellin amplitude may in general have more than one series of poles. We present a few examples of Mellin amplitudes for tree-level Witten diagrams and tree-level conformal Feynman integrals with fermionic legs, which illustrate the general properties.