Solutions of free higher spins in AdS

We consider free massive and massless higher integer spins in AdS backgrounds in general D dimensions. We obtain the solutions corresponding to the highest-weight state of the spin-ℓ representations of the SO(2,D−1) isometry groups. The solution for the spin-ℓ field is expressed recursively in terms of that for the spin-(ℓ−1). Thus starting from the explicit spin-0, all the higher-spin solutions can be obtained. These solutions allow us to derive the generalized Breitenlohner-Freedman bound, and analyze the asymptotic falloffs. In particular, solutions with negative mass square in general have falloffs slower than those of the Schwarzschild AdS black holes in the AdS boundaries.