  We develop the embedding formalism to describe symmetric traceless tensors in
Anti-de Sitter space. We use this formalism to construct the bulk-to-bulk
propagator of massive spin J fields and check that it has the expected short
distance and massless limits. We also and a split representation for the
bulk-to-bulk propagator, by writing it as an integral over the boundary of the
product of two bulk-to-boundary propagators. We exemplify the use of this
representation with the computation of the conformal partial wave decomposition
of Witten diagrams. In particular, we determine the Mellin amplitude associated
to AdS graviton exchange between minimally coupled scalars of general
dimension, including the regular part of the amplitude.
