KK spectroscopy of type IIB supergravity on AdS5 × T11

We give full details for the computation of the Kaluza--Klein mass spectrumof Type IIB Supergravity on AdS_5 x T^{11}, with T^{11}=SU(2)xSU(2)/U(1), thathas recently lead to both stringent tests and interesting predictions on theAdS_5/CFT_4 correspondence for N=1 SCFT's (hep-th/9905226). We exhaustivelyexplain how KK states arrange into SU(2,2|1) supermultiplets, and stress somerelevant features of the T^{11} manifold, such as the presence of topologicalmodes in the spectrum originating from the existence of non-trivial 3-cycles.The corresponding Betti vector multiplet is responsible for the extra baryonicsymmetry in the boundary CFT. More generally, we use the simple T^{11} coset asa laboratory to revive the technique and show the power of KK harmonicexpansion, in view of the present attempts to probe along the same lines alsoM-theory compactifications and the AdS_4/CFT_3 map.Comment: 41 pages, LaTex + latexsy