M-theory on AdS(4) x M-111: the complete Osp (2 vertical bar 4) x SU (3) xSU (2) spectrum from harmonic analysis

We reconsider the Kaluza-Klein compactifications of D = 11 supergravity on AdS(4) x (G/H)(7) manifolds that were classified in the eighties, in the mo dern perspective of AdS(4)/CFT3 correspondence. We focus on one of the thre e N = 2 cases: (G/H)(7) = M-111 = SU(3) x SU(2) x U(1)/SU(2) x U(1)' x U(1) ". Relying on the systematic use of the harmonic analysis techniques develo ped in the eighties by one of us (P. Fre) with R. D'Auria, we derive the co mplete spectrum of long, short and massless Osp(2/4) x SU(3) x SU(2) unitar y irreducible representations obtained in this compactification. Our result also provides a general scheme for the other N = 2 compactifications, Furt hermore, 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 mu ch more stringent proof of the AdS/CFT correspondence than in the S-7 case, since the structure of the superconformal field theory on the M2-brane wor ld volume must be such as to reproduce, at the level of composite operators , the flavor group representations, the conformal dimensions and the hyperc harges that we obtain in the present article. The investigation of this mat ch is left to future publications. Here we provide an exhaustive constructi on of the Kaluza-Klein side of our spectroscopy. (C) 1999 Published by Else vier Science B.V. All rights reserved.