Holographic dual of the five-point conformal block

Abstract

We present the holographic object which computes the five-point global conformal block in arbitrary dimensions for external and exchanged scalar operators. This object is interpreted as a weighted sum over infinitely many five-point geodesic bulk diagrams. These five-point geodesic bulk diagrams provide a generalization of their previously studied four-point counterparts. We prove our claim by showing that the aforementioned sum over geodesic bulk diagrams is the appropriate eigenfunction of the conformal Casimir operator with the right boundary conditions. This result rests on crucial inspiration from a much simpler $p$-adic version of the problem set up on the Bruhat-Tits tree.

20 pages + references, several figures. v2: Minor typos fixed, matches published version

References in corpus (8)

• Writing CFT correlation functions as AdS scattering amplitudes
• Witten Diagrams for Torus Conformal Blocks
• Many-point classical conformal blocks and geodesic networks on the hyperbolic plane
• Geodesic bulk diagrams on the Bruhat-Tits tree
• Simplicity in AdS Perturbative Dynamics
• Geodesic Witten diagrams with anti-symmetric exchange
• Mellin-(Schwinger) representation of One-loop Witten diagrams in AdS
• Bulk fields from the boundary OPE

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• Semiclassical torus blocks in the t-channel
• A geodesic Witten diagram description of holographic entanglement entropy and its quantum corrections
• Wilson lines construction of $\mathfrak{osp}(1|2)$ conformal blocks
• The boundary theory of a spinor field theory on the Bruhat-Tits tree
• Conformal Blocks in Two and Four Dimensions from Oscillator Representations
• Large-$c$ conformal $(n\le 6)$-point blocks with superlight weights and holographic Steiner trees
• All Global One- and Two-Dimensional Higher-Point Conformal Blocks
• Finite Temperature at Finite Places
• How to Succeed at Witten Diagram Recursions without Really Trying
• On-shell Correlators and Color-Kinematics Duality in Curved Symmetric Spacetimes
• Analytic Studies of Fermions in the Conformal Bootstrap