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

TL;DR

This paper identifies the gauge dual of a specific warped AdS_4 background with a U(N)^3 superconformal Chern-Simons theory, and computes the spectrum of spin-2 Kaluza-Klein modes, linking supergravity and field theory details.

Contribution

It establishes the precise gauge dual of a warped AdS_4 background with a squashed and stretched S^7, including detailed operator correspondence and KK spectrum calculations.

Findings

The gauge dual is a U(N)^3 superconformal Chern-Simons theory with specific matter content.

The spectrum of spin-2 KK modes is computed, revealing their dependence on quantum numbers.

Operator dimensions in the dual field theory are determined from supergravity analysis.

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.