On Feynman rules for Mellin amplitudes in AdS/CFT

Abstract

The computation of CFT correlation functions via Witten diagrams in AdS space can be simplified via the Mellin transform. Recently a set of Feynman rules for tree-level Mellin space amplitudes has been proposed for scalar theories. In this note we derive these rules by explicitly evaluating all of the relevant Witten diagram integrals for the scalar phi^n theory. We also check that the rules reduce to the usual Feynman rules in the flat space limit.

minor corrections, published version

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• TASI lectures on AdS/CFT
• Spinning AdS Loop Diagrams: Two Point Functions
• Physics of the Inverted Harmonic Oscillator: From the lowest Landau level to event horizons
• Mellin Amplitudes for Dual Conformal Integrals
• Star Integrals, Convolutions and Simplices
• A multipoint conformal block chain in $d$ dimensions
• On Mellin Amplitudes in SCFTs with Eight Supercharges
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• Gravity with a cosmological constant from rational curves
• Towards Feynman rules for conformal blocks
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• Feynman Rules for Scalar Conformal Blocks
• Exploring Perturbative Conformal Field Theory in Mellin space
• Minkowski Conformal Blocks and the Regge Limit for SYK-like Models
• Bootstrapping Witten diagrams via differential representation in Mellin space
• Recursion Relations in $p$-adic Mellin Space
• Loops, Polytopes and Splines
• Simplifying instanton corrections to N=4 SYM correlators
• A Universal Formula for the Stress-Tensor Contribution to Scalar Four-Point Functions
• Towards holographic higher-spin interactions: Four-point functions and higher-spin exchange
• An Elliptic One-Loop Amplitude in Anti-de-Sitter Space
• Propagators in AdS for higher-derivative and nonlocal gravity: Heat kernel approach
• A Holographic Holographic Bound and the Black Hole S-Matrix
• Constructing CFTs from AdS flows