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.
Highlights
From the pioneering work of Mack [1, 2], followed up on later by Penedones and several others [3,4,5,6,7], we understand that Mellin space provides us with a natural representation to study conformal correlation functions
We have introduced Mellin amplitudes associated with correlators of spin half fermions and scalars
Such Mellin amplitudes have multiple components, each component being associated with an element of a chosen basis of tensor structures
Summary
From the pioneering work of Mack [1, 2], followed up on later by Penedones and several others [3,4,5,6,7], we understand that Mellin space provides us with a natural representation to study conformal correlation functions. The three point function of two fermions and a boson has multiple tensor structures This results in each component of the Mellin amplitude having more than one distinct series (two in our case) of poles corresponding to each primary operator exchanged in the OPE in a given channel. It must be noted that the pole structure of the Mellin amplitude is related to the choice of basis and is tunable as such After this preliminary analysis of the properties of the Mellin amplitude, we compute some Mellin amplitudes corresponding to tree level Witten diagrams and tree level conformal Feynman integrals. These examples illustrate the generic predictions on the pole structure considering the parity of the three point functions in each case. Calculations, methods and a short review of fermions in AdS are provided in the appendices
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
