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

Abstract

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 , B2 transforming in the , C1 in the and C2 in the 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) 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.