Spinning AdS Propagators

TL;DR

This paper develops a formalism for symmetric traceless tensors in AdS space to construct and analyze spinning propagators, including their split representation and applications to conformal partial waves and Mellin amplitudes.

Contribution

It introduces a new embedding formalism for symmetric traceless tensors and constructs the bulk-to-bulk propagator for massive spin J fields in AdS.

Findings

Constructed the bulk-to-bulk propagator with correct limits.

Developed a split representation as an integral over boundary propagators.

Computed the Mellin amplitude for AdS graviton exchange.

Abstract

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.