Towards Spinning Mellin Amplitudes

Abstract

We construct the Mellin representation of four point conformal correlation function with external primary operators with arbitrary integer spacetime spins, and obtain a natural proposal for spinning Mellin amplitudes. By restricting to the exchange of symmetric traceless primaries, we generalize the Mellin transform for scalar case to introduce discrete Mellin variables for incorporating spin degrees of freedom. Based on the structures about spinning three and four point Witten diagrams, we also obtain a generalization of the Mack polynomial which can be regarded as a natural kinematical polynomial basis for computing spinning Mellin amplitudes using different choices of interaction vertices.

arXiv comment32 pages, 2 figures, v2: typos corrected, clarification added, references updated, to appear in NPB

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Cited by in corpus (18)

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• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
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• Nonperturbative Mellin Amplitudes: Existence, Properties, Applications
• On Superconformal Four-Point Mellin Amplitudes in Dimension $d>2$
• Spinning Mellin Bootstrap: Conformal Partial Waves, Crossing Kernels and Applications
• The Cosmological Bootstrap: Spinning Correlators from Symmetries and Factorization
• Higher-Point Conformal Blocks in the Comb Channel
• On Mellin Amplitudes in SCFTs with Eight Supercharges
• New Methods for Conformal Correlation Functions
• Towards Feynman rules for conformal blocks
• Efficient Rules for All Conformal Blocks
• Four point functions in CFT's with slightly broken higher spin symmetry
• On Conformal Block, Crossing Kernel and Multi-variable Hypergeometric Functions
• Conformal Two-Point Correlation Functions from the Operator Product Expansion
• Mellin amplitudes for $Ad{S}_3\times S^3$
• Superconformal Block from Holographic Geometry
• How to Succeed at Witten Diagram Recursions without Really Trying