M -theory on AdS_4 x Q^{111}: The complete Osp(2|4) x SU(2) x SU(2) x SU(2) spectrum from harmonic analysis

Abstract

In this paper by means of harmonic analysis we derive the complete spectrum of Osp(2|4) x SU(2) x SU(2) x SU(2) multiplets that one obtains compactifying D=11 supergravity on the homogeneous space Q^{111}. In particular we analyze the structure of the short multiplets and compare them with the corresponding composite operators of the N=2 conformal field theory dual to such a compactification, found in a previous publication. We get complete agreement between the quantum numbers of the supergravity multiplets on one side and those of the conformal operators on the other side, 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 they are, the exact values of the hypercharge and of the energy for each multiplet.