# Spinning Geodesic Witten Diagrams

## TL;DR

This paper generalizes the geodesic Witten diagram formalism to compute four-point conformal blocks for symmetric traceless operators of any spin using integrals over geodesics in Anti-de Sitter space, connecting to shadow operator methods.

## Contribution

It introduces a new integral representation for spinning conformal blocks in AdS, extending previous scalar cases, and identifies a basis of bulk vertices for boundary three-point structures.

## Key findings

- Derived explicit integral expressions for spinning conformal blocks.
- Established a link between geodesic Witten diagrams and shadow formalism.
- Provided a basis for bulk interaction vertices for arbitrary spin.

## 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.