Saturating the unitarity bound in AdS/CFT_(AdS)

We investigate the holographic description of CFTs defined on the cylinder and on AdS, which include an operator saturating the unitarity bound. The standard Klein-Gordon field with the corresponding mass and boundary conditions on global AdS_(d+1) and on an AdS_(d+1) geometry with AdS_d conformal boundary contains ghosts. We identify a limit in which the singleton field theory is obtained from the bulk theory with standard renormalized inner product, showing that a unitary bulk theory corresponding to an operator which saturates the unitarity bound can be formulated and that this yields a free field on the boundary. The normalizability issues found for the standard Klein-Gordon field on the geometry with AdS_d conformal boundary are avoided for the singleton theory, which offers interesting prospects for multi-layered AdS/CFT.