Geodesic Witten diagrams with an external spinning field

TL;DR

This paper establishes a precise correspondence between geodesic Witten diagrams and conformal blocks involving external spinning fields in AdS/CFT, deriving new expressions and confirming their equivalence through multiple methods.

Contribution

It derives explicit formulas for conformal partial waves with external spin-1 and arbitrary symmetric traceless tensor fields, demonstrating their equivalence to geodesic Witten diagram amplitudes.

Findings

Derived conformal partial wave expression for external spin-1 fields.

Extended the construction to arbitrary symmetric traceless tensor fields.

Confirmed the equivalence using conformal Casimir equations.

Abstract

We explore AdS/CFT correspondence between geodesic Witten diagrams and conformal blocks (conformal partial waves) with an external symmetric traceless tensor field. We derive an expression for the conformal partial wave with an external spin-1 field and show that this expression is equivalent to the amplitude of the geodesic Witten diagram. We also show the equivalence by using conformal Casimir equation in embedding formalism. Furthermore, we extend the construction of the amplitude of the geodesic Witten diagram to an external arbitrary symmetric traceless tensor field. We show our construction agrees with the known result of the conformal partial waves.