\(M\)-theory on \(\text{AdS}_4\times Q^{111}\): The complete \(\text{Osp}(2|4)\times \text{SU}(2)\times \text{SU}(2)\times \text{SU}(2)\) spectrum from harmonic analysis (Q2752491)

Using the basic principle of the AdS/CFT correspondence, which states that every consistent \(M\)-theory or type II background with metric \(\text{AdS}_{p+2}\times M^{d-p-2}\) in \(d\)-dimensions is associated with a conformal quantum field theory living on the boundary of \(\text{AdS}_{p+2}\), the case \(p=2\) when \(M\) is a coset manifold \(G/H\) with \(N=2\) supersymmetry is investigated. The complete spectrum of \(\text{Osp}( 2|4) \times \text{SU}(2)\times \text{SU}(2)\times \text{SU}(2)\) multiplets that one obtains compactifying \(D=11\) supergravity on the homogeneous space \(Q^{111}\) being the quotient of \(G=\text{SU}(2)\times \text{SU}(2)'\times \text{SU}(2)^{\prime \prime }\times U(1)\) by the action of its subgroup \(H=U(1)'\times U(1)''\times U(1)'''\) is derived by means of harmonic analysis. The structure of the short multiplets is analyzed, and they are compared with the corresponding composite operators of the \(N=2\) conformal field theory dual to such a compactification. 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, is achieved.