Geodesic Witten diagrams with anti-symmetric exchange

TL;DR

This paper establishes the correspondence between conformal partial waves and geodesic Witten diagrams with anti-symmetric exchange in AdS/CFT, introducing a new formalism and exploring their connections.

Contribution

It introduces the embedding space formalism for anti-symmetric fields and proves the geodesic Witten diagram's compliance with the conformal Casimir equation.

Findings

Confirmed the geodesic Witten diagram satisfies the conformal Casimir equation.

Established the connection between geodesic Witten diagrams and the shadow formalism.

Extended the analysis to 3pt geodesic Witten diagrams and mixed-symmetric tensors.

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.