  In this work we expand on the holographic description of CFTs on de Sitter
(dS) and anti-de Sitter (AdS) spacetimes and examine how violations of the
unitarity bound in the boundary theory are recovered in the bulk physics. To
this end we consider a Klein-Gordon field on AdS_(d+1) conformally compactified
such that the boundary is (A)dS_d, and choose masses and boundary conditions
such that the corresponding boundary operator violates the CFT unitarity bound.
The setup in which the boundary is AdS_d exhibits a particularly interesting
structure, since in this case the boundary itself has a boundary. The bulk
theory turns out to crucially depend on the choice of boundary conditions on
the boundary of the AdS_d slices. Our main result is that violations to the
unitarity bound in CFTs on dS_d and AdS_d are reflected in the bulk through the
presence of ghost excitations. In addition, analyzing the setup with AdS_d on
the boundary allows us to draw conclusions on multi-layered AdS/CFT-type
dualities.
