Higher-Point Conformal Blocks in the Comb Channel

Abstract

We compute $M$-point conformal blocks with scalar external and exchange operators in the so-called comb configuration for any $M$ in any dimension $d$. Our computation involves repeated use of the operator product expansion to increase the number of external fields. We check our results in several limits and compare with the expressions available in the literature when $M=5$ for any $d$, and also when $M$ is arbitrary while $d=1$.

arXiv comment1+27 pages

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Cited by in corpus (23)

• Multipoint Bootstrap I: Light-Cone Snowflake OPE and the WL Origin
• OPE statistics from higher-point crossing
• Gaudin Models and Multipoint Conformal Blocks: General Theory
• Scattering Equations in AdS: Scalar Correlators in Arbitrary Dimensions
• From Gaudin Integrable Models to $d$-dimensional Multipoint Conformal Blocks
• Gaudin Models and Multipoint Conformal Blocks II: Comb channel vertices in 3D and 4D
• Recursion relations for 5-point conformal blocks
• Seven-Point Conformal Blocks in the Extended Snowflake Channel and Beyond
• Gaudin Models and Multipoint Conformal Blocks III: Comb channel coordinates and OPE factorisation
• Six-Point Conformal Blocks in the Snowflake Channel
• Towards Feynman rules for conformal blocks
• Shadow Celestial Amplitude
• Improving the five-point bootstrap
• Lining up a Positive Semi-Definite Six-Point Bootstrap
• Efficient Rules for All Conformal Blocks
• Feynman Rules for Scalar Conformal Blocks
• Dimensional reduction of higher-point conformal blocks
• Conformal partial waves in momentum space
• More on Wilson toroidal networks and torus blocks
• Stampedes II: Null Polygons in Conformal Gauge Theory
• Conformal Blocks in Two and Four Dimensions from Oscillator Representations
• Sparsity in the numerical six-point bootstrap
• Spinors and conformal correlators