A note on causality in the bulk and stability on the boundary

By carefully analyzing the radial part of the wave-equation for a scalar field in AdS_d+1, we show that for a particular range of boundary conditions on the scalar field, the radial spectrum contains a bound state. Using the AdS/CFT correspondence, we interpret this peculiar phenomenon as being dual to an unstable double trace deformation of the boundary conformal field theory. We thus show how the bulk theory holographically detects whether a boundary perturbation is stable.