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

In this paper we derive, by means of harmonic analysis, the complete spectr um of O sp (2 \4) x SU (2) x SU (2) x SU (2) multiplets from which one obta ins compactifying D = 11 supergravity on the homogeneous space Q(111). In p articular, we analyse the structure of the short multiplets and compare the m to the corresponding composite operators of the N = 2 conformal field the ory dual to such a compactification, found in a previous publication. We fi nd complete agreement between the quantum numbers of the supergravity multi plets on one hand and those of the conformal operators on the other hand, c onfirming the structure of the conjectured SCFT. However, the determination of the actual spectrum by harmonic analysis teaches us a lot more: indeed we find out which multiplets are present for each representation of the iso metry group, how many there are, the exact values of the hypercharge and of the `energy' for each multiplet.