The group approach to AdS space propagators

TL;DR

This work develops a group-theoretic framework to construct AdS space propagators by composing two bulk-to-boundary intertwiners and integrating over a boundary point, yielding bulk-to-bulk two-point functions as representation-theoretic objects. The method naturally produces both the direct propagator and its shadow partner, reflecting conformal field theory structure. By reducing boundary convolution integrals from Appell F4 functions to Legendre functions of the second kind, the authors obtain explicit expressions for scalar, vector, and rank-2 symmetric traceless tensor propagators in AdS, expressed via geodesic-distance dependent functions. The approach emphasizes representation theory as a unifying tool for AdS/CFT correlators across tensor ranks and offers a constructive path toward higher-spin AdS theories without relying on a specific Lagrangian.

Abstract

We show that AdS two-point functions can be obtained by connecting two points in the interior of AdS space with one point on its boundary by a dual pair of Dobrev's boundary-to-bulk intertwiners and integrating over the boundary point.