Spinning Witten diagrams

We develop a systematic framework to compute the conformal partial wave expansions (CPWEs) of tree-level four-point Witten diagrams with totally symmetric external fields of arbitrary mass and integer spin in AdS(d+1). As an intermediate step, we identify convenient bases of three-point bulk and boundary structures to invert linear map between spinning three-point conformal structures and spinning cubic couplings in AdS. Given a CFTd, this provides the complete holographic reconstruction of all cubic couplings involving totally symmetric fields in the putative dual theory on AdS(d+1). Employing this framework, we determine the CPWE of a generic four-point exchange Witten diagram with spinning exchanged field. As a concrete application, we compute all four-point exchange Witten diagrams in the type A higher-spin gauge theory on AdS(d+1), which is conjectured to be dual to the free scalar O (N) model.