The gauge dual of a warped product of AdS4 and a squashed and stretched seven-manifold

Corrado, Pilch and Warner found in 2001 the second 11-dimensional solution where the deformed geometry of S⁷ in the lift contains S² × S². We identify the gauge dual of this background with the theory described by Franco, Klebanov and Rodriguez-Gomez recently. It is the U(N) × U(N) × U(N) gauge theory with two SU(2) doublet chiral fields B₁ transforming in the ({\bf N}, \overline{\bf N}, {\bf 1}), B₂ transforming in the ({\bf 1}, {\bf N}, \overline{\bf N}), C₁ in the ({\bf 1}, \overline{\bf N}, {\bf N}) and C₂ in the (\overline{\bf N}, {\bf N}, {\bf 1}) as well as an adjoint field Φ in the (1, adj, 1) representation. By adding the mass term for adjoint field Φ, the detailed correspondence between fields of AdS₄ supergravity and composite operators of the IR field theory is determined. Moreover, we compute the spin-2 KK modes around a warped product of AdS₄ and a squashed and stretched seven-manifold. This background with global SU(2) × SU(2) × U(1)_R symmetry is related to a U(N) × U(N) × U(N) {\cal N}=2 superconformal Chern-Simons matter theory with eighth-order superpotential and Chern-Simons level (1, 1, -2). The mass-squared in AdS₄ depends on SU(2) × SU(2) × U(1)_R quantum numbers and the KK excitation number. The dimensions of spin-2 operators are found.