Geodesic Witten diagrams with anti-symmetric exchange

Abstract

We show the AdS/CFT correspondence between the conformal partial wave and the geodesic Witten diagram with anti-symmetric exchange. To this end, we introduce the embedding space formalism for anti-symmetric fields in AdS. Then we prove that the geodesic Witten diagram satisfies the conformal Casimir equation and the appropriate boundary condition. Furthermore, we discuss the connection between the geodesic Witten diagram and the shadow formalism by using the split representation of harmonic function for anti-symmetric fields. We also discuss the 3pt geodesic Witten diagrams and its extension to the mixed-symmetric tensors.

arXiv comment17 pages, 2 figures

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• Towards Feynman rules for conformal blocks
• Fermions in Geodesic Witten Diagrams
• Scalar Blocks as Gravitational Wilson Networks
• Regge conformal blocks from the Rindler-AdS black hole and the pole-skipping phenomena
• Comments on spinning OPE blocks in AdS${}_3$/CFT${}_2$
• A Large Twist Limit for Any Operator