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

TL;DR

This work derives the full Kaluza-Klein spectrum of $D=11$ supergravity on $AdS_4\times Q^{111}$ via harmonic analysis, yielding the complete set of $Osp(2|4)\times SU(2)\times SU(2)\times SU(2)$ multiplets with explicit energies $E_0$ and hypercharges $y_0$. By constructing and solving the zero-, one-, two-, three-form, and spinor mass operators on $Q^{111}$, the authors classify the spectrum into long, short, and massless ${\cal N}=2$ multiplets, including Betti multiplets tied to nontrivial cohomology. The results exhibit exact agreement with the predicted dual ${\cal N}=2$ SCFT, validating the AdS/CFT correspondence for this Sasaki–Einstein background and providing detailed multiplet-by-multiplet quantum numbers, not just representations. The analysis highlights how the geometry of $Q^{111}$ determines the KK masses and multiplet shortening, offering a precise framework for similar Sasakian compactifications and their SCFT duals.

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.