Dressing in AdS and a Conformal Bethe-Salpeter Equation

We initiate the study of Dyson equations of perturbative QFT in AdS and their consequences for large-N CFT. We show that the dressed one-particle AdS propagator features wavefunction renormalization and operator mixing, giving rise to finite corrections to OPE data. We show how the resummation of 1/N effects in the CFT emerges from the dressing in AdS. When a boundary-to-bulk propagator is dressed by propagators whose sum of conformal dimensions is lower than the main dimension, it cannot map onto a CFT source; we relate this to an AdS/CFT version of particle instability. We investigate the dressing of the two-particle propagator and obtain a conformal Bethe-Salpeter equation for the conformal partial wave of a "bound state" operator. We provide a self-contained calculation for the case of a ladder kernel. We show that a bound state with conformal dimension equal to the sum of its constituents plus a 1/N^2-suppressed "binding energy" emerges. Resummation of the Dyson equations is essential for deriving these results.