  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.
