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

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Abstract
In this paper we derive, by means of harmonic analysis, the complete spectrum of Osp(2|4)×SU(2)×SU(2)×SU(2) multiplets from which one obtains compactifying D = 11 supergravity on the homogeneous space Q111. In particular, we analyse the structure of the short multiplets and compare them to the corresponding composite operators of the = 2 conformal field theory dual to such a compactification, found in a previous publication. We find complete agreement between the quantum numbers of the supergravity multiplets on one hand and those of the conformal operators on the other hand, confirming 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 isometry group, how many there are, the exact values of the hypercharge and of the `energy' for each multiplet.
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