from harmonic analysis ∗

We reconsider the Kaluza Klein compactifications of D = 11 supergravity on AdS4 × (G/H)7 manifolds that were classified in the eighties, in the modern perspective of AdS4/CFT3 correspondence. We focus on one of the three N = 2 cases: (G/H)7 = M111 = SU(3)× SU(2)×U(1)/SU(2)×U(1)′ ×U(1)′′. Relying on the systematic use of the harmonic analysis techniques developed in the eighties by one of us (P. Fré) with R. D’Auria, we derive the complete spectrum of long, short and massless Osp(2|4)×SU(3)× SU(2) unitary irreducible representations obtained in this compactification. Our result also provides a general scheme for the other N = 2 compactifications. Furthermore it is a necessary comparison term in the AdS4/CFT3 correspondence: the complete AdS/CFT match of the spectra that we obtain will provide a much more stringent proof of the AdS/CFT correspondence than in the S7 case, since the structure of the superconformal field theory on the M2–brane world volume must be such as to reproduce, at the level of composite operators, the flavor group representations, the conformal dimensions and the hypercharges that we obtain in the present article. The investigation of this match is left to future publications. Here we provide an exhaustive construction of the Kaluza Klein side of our spectroscopy. ∗ Supported in part by EEC under TMR contract ERBFMRX-CT96-0045