Recursion relations for 5-point conformal blocks

Abstract

We consider 5-point functions in conformal field theories in d > 2 dimensions. Using weight-shifting operators, we derive recursion relations which allow for the computation of arbitrary conformal blocks appearing in 5-point functions of scalar operators, reducing them to a linear combination of blocks with scalars exchanged. We additionally derive recursion relations for the conformal blocks which appear when one of the external operators in the 5-point function has spin 1 or 2. Our results allow us to formulate positivity constraints using 5-point functions which describe the expectation value of the energy operator in bilocal states created by two scalars.

104 pages, 1 attached Mathematica notebook; V2: small adjustments, references added; V3: clarifications and some formulas corrected

References in corpus (10)

• Conformal collider physics: Energy and charge correlations
• Bootstrapping Mixed Correlators in the 3D Ising Model
• Bounds on OPE Coefficients from Interference Effects in the Conformal Collider
• Multipoint Bootstrap I: Light-Cone Snowflake OPE and the WL Origin
• Holographic dual of the five-point conformal block
• 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
• Dimensional reduction of higher-point conformal blocks
• The Inversion Formula and 6j Symbol for 3d Fermions

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• Shadow Celestial Amplitude
• Feynman Rules for Scalar Conformal Blocks
• Exact Diagonalization, Matrix Product States and Conformal Perturbation Theory Study of a 3D Ising Fuzzy Sphere Model
• Universal Spinning Casimir Equations and Their Solutions
• Spinors and conformal correlators
• Recursive structure of the Gauß hypergeometric function and boundary/crosscap conformal block