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 KleinGordon field with the corresponding mass and boundary conditions on global AdSd+1 and on an AdSd+1 geometry with AdSd 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 AdSd conformal boundary are avoided for the singleton theory, which offers interesting prospects for multi-layered AdS/CFT.