Mellin Amplitudes for Fermionic Conformal Correlators

Josua Faller, Sourav Sarkar

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