Towards Feynman rules for conformal blocks

Abstract

We conjecture a simple set of "Feynman rules" for constructing $n$-point global conformal blocks in any channel in $d$ spacetime dimensions, for external and exchanged scalar operators for arbitrary $n$ and $d$. The vertex factors are given in terms of Lauricella hypergeometric functions of one, two or three variables, and the Feynman rules furnish an explicit power-series expansion in powers of cross-ratios. These rules are conjectured based on previously known results in the literature, which include four-, five- and six-point examples as well as the $n$-point comb channel blocks. We prove these rules for all previously known cases, as well as for a seven-point block in a new topology and the even-point blocks in the "OPE channel." The proof relies on holographic methods, notably the Feynman rules for Mellin amplitudes of tree-level AdS diagrams in a scalar effective field theory, and is easily applicable to any particular choice of a conformal block.

arXiv comment59 pages + appendices, several figures

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Cited by in corpus (12)

• Gaudin Models and Multipoint Conformal Blocks: General Theory
• Gaudin Models and Multipoint Conformal Blocks II: Comb channel vertices in 3D and 4D
• Recursion relations for 5-point conformal blocks
• Gaudin Models and Multipoint Conformal Blocks III: Comb channel coordinates and OPE factorisation
• Six-point functions and collisions in the black hole interior
• Shadow Celestial Amplitude
• Improving the five-point bootstrap
• Feynman Rules for Scalar Conformal Blocks
• Dimensional reduction of higher-point conformal blocks
• Conformal partial waves in momentum space
• Conformal Blocks in Two and Four Dimensions from Oscillator Representations
• Operator growth and black hole formation