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.

arXiv comment20 pages + references, several figures. v2: Minor typos fixed, matches published version

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• Towards the higher point holographic momentum space amplitudes II: Gravitons
• From Gaudin Integrable Models to $d$-dimensional Multipoint Conformal Blocks
• Higher-Point Conformal Blocks in the Comb Channel
• On the Virasoro six-point identity block and chaos
• Gaudin Models and Multipoint Conformal Blocks II: Comb channel vertices in 3D and 4D
• A multipoint conformal block chain in $d$ dimensions
• 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
• p-Adic open string amplitudes with Chan-Paton factors coupled to a constant B-field
• Opacity from Loops in AdS
• Towards Feynman rules for conformal blocks
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• Holographic variables for CFT${}_2$ conformal blocks with heavy operators
• Improving the five-point bootstrap
• Feynman Rules for Scalar Conformal Blocks
• Dimensional reduction of higher-point conformal blocks
• More on Wilson toroidal networks and torus blocks
• Semiclassical torus blocks in the t-channel
• A geodesic Witten diagram description of holographic entanglement entropy and its quantum corrections
• The boundary theory of a spinor field theory on the Bruhat-Tits tree
• Wilson lines construction of $\mathfrak{osp}(1|2)$ conformal blocks
• 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
• Reparametrization mode Ward Identities and chaos in higher-pt. correlators in CFT${}_2$
• 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