Spinning Geodesic Witten Diagrams

Abstract

We present an expression for the four-point conformal blocks of symmetric traceless operators of arbitrary spin as an integral over a pair of geodesics in Anti-de Sitter space, generalizing the geodesic Witten diagram formalism of Hijano et al [arXiv:1508.00501] to arbitrary spin. As an intermediate step in the derivation, we identify a convenient basis of bulk three-point interaction vertices which give rise to all possible boundary three point structures. We highlight a direct connection between the representation of the conformal block as a geodesic Witten diagram and the shadow operator formalism.

28+6 pages, 8 figures

References in corpus (10)

• Writing CFT correlation functions as AdS scattering amplitudes
• Bounds on 4D Conformal and Superconformal Field Theories
• Spinning AdS Propagators
• Bounds in 4D Conformal Field Theories with Global Symmetry
• Central Charge Bounds in 4D Conformal Field Theory
• Spinning Witten Diagrams
• Harmony of Spinning Conformal Blocks
• Higher-Spin Algebras, Holography and Flat Space
• Anatomy of Geodesic Witten Diagrams
• Geodesic Diagrams, Gravitational Interactions & OPE Structures

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• Holographic OPE Coefficients from AdS Black Holes with Matters
• A multipoint conformal block chain in $d$ dimensions
• Double-Trace Deformations of Conformal Correlations
• Seven-Point Conformal Blocks in the Extended Snowflake Channel and Beyond
• Six-Point Conformal Blocks in the Snowflake Channel
• New Methods for Conformal Correlation Functions
• Towards Feynman rules for conformal blocks
• Fermions in Geodesic Witten Diagrams
• Scalar Blocks as Gravitational Wilson Networks
• Efficient Rules for All Conformal Blocks
• Regge conformal blocks from the Rindler-AdS black hole and the pole-skipping phenomena
• Higher-spin gravity's "string": new gauge and proof of holographic duality for the linearized Didenko-Vasiliev solution
• Bulk locality and gauge invariance for boundary-bilocal cubic correlators in higher-spin gravity
• The gravity dual of Lorentzian OPE blocks
• More on Boundary Holographic Witten Diagrams