Beyond the unitarity bound in AdS/CFT(A)dS

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.