The Gauge Dual of A Warped Product of AdS_4 and A Squashed and Stretched Seven-Manifold

Abstract

Corrado, Pilch and Warner in 2001 have found the second 11-dimensional solution where the deformed geometry of S^7 in the lift contains S^2 x S^2. We identify the gauge dual of this background with the theory described by Franco, Klebanov and Rodriguez-Gomez recently. It is the U(N) x U(N) x U(N) gauge theory with two SU(2) doublet chiral fields B_1 transforming in the (N, Nbar, 1), B_2 transforming in the (1, N, Nbar), C_1 in the (1, Nbar, N) and C_2 in the (Nbar, N, 1) as well as an adjoint field \Phi in the (1, adj, 1) representation. By adding the mass term for adjoint field \Phi, the detailed correspondence between fields of AdS_4 supergravity and composite operators of the IR field theory is determined. Moreover, we compute the spin-2 KK modes around a warped product of AdS_4 and a squashed and stretched seven-manifold. This background with global SU(2) x SU(2) x U(1)_R symmetry is related to a U(N) x U(N) x U(N) N=2 superconformal Chern-Simons matter theory with eighth-order superpotential and Chern-Simons level (1,1,-2). The mass-squared in AdS_4 depends on SU(2) x SU(2) x U(1)_R quantum numbers and KK excitation number. The dimensions of spin-2 operators are found.