Mellin Amplitudes for Fermionic Conformal Correlators

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.

arXiv comment28 pages + Appendices, 8 figures

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• A Study of Quantum Field Theories in AdS at Finite Coupling
• On the Polyakov-Mellin bootstrap
• On Superconformal Four-Point Mellin Amplitudes in Dimension $d>2$
• Spinning Mellin Bootstrap: Conformal Partial Waves, Crossing Kernels and Applications
• AdS${}_4$/CFT${}_3$ from Weak to Strong String Coupling
• A Crossing-Symmetric OPE Inversion Formula
• Higher-Point Conformal Blocks in the Comb Channel
• Fermions in AdS and Gross-Neveu BCFT
• On Mellin Amplitudes in SCFTs with Eight Supercharges
• Towards Bootstrapping RG flows: Sine-Gordon in AdS
• New Methods for Conformal Correlation Functions
• Towards Feynman rules for conformal blocks
• Crossing antisymmetric Polyakov blocks + Dispersion relation
• Efficient Rules for All Conformal Blocks
• Four point functions in CFT's with slightly broken higher spin symmetry
• Mellin amplitudes for $Ad{S}_3\times S^3$
• Bootstrapping AdS${}_2\times$ S${}^2$ hypermultiplets: hidden four-dimensional conformal symmetry