I. INTRODUCTION Recently we have seen great progress on our understanding of field theory duals for various AdS$_{4}$ backgrounds in string or M-theory. Most notable is the discovery of N = 6 supersymmetric Chern-Simons-matter theories which provide conformal field theory duals for AdS$_{4}$ × S $^{7}$/$_{Z}$$_{k}$ [1]. This three-dimensional field theory has U ( N ) × U ( N ) gauge symmetry with Chern-Simons (CS) kinetic terms of quantized level ( k, − k ). The interaction is also described by a quartic superpotential. In fact, as a quiver guage theory the data is exactly the same as the well-known conifold theory in four-dimensions [2], apart from the extra information on CS levels. It is an important issue how to generalize this duality to other backgrounds AdS$_{4}$ × Y$_{7}$ . In this paper, we are particularly interested in the examples which preserve N = 2, or eight supercharges. Mathematically Y$_{7}$ is then required to be Sasaki-Einstein, and we choose the so-called M 1 , 1 , 1 space [3]. It is constructed as U (1)-fibration over a six-dimensional K¨ ahler- Einstein manifold CP 2 ×$_{CP}$ $^{1}$. The dual field theory is thus expected to enjoy SU (3) × SU (2) × U (1) global symmetry, where the U (1) part is the usual R-symmetry. In order to establish the duality relation, we need the Kaluza-Klein spectrum of 11- dimensional supergravity on M 1 , 1 , $^{1}$. It is computed in [4], and a three-dimensional quiver gauge theory was proposed as the dual of AdS$_{4}$ × M 1 , 1 , 1 in [5], but a consistent superpotential could not be written down. Now with the new insight of Chern-Simons theories without the usual second-order Maxwell-type kinetic terms, we have a more reliable candidate. The CS duals have been given for a general class of the so-called Y $^{p,q}$($_{CP}$ $^{2}$) metrics [6, 7]. For our interest here the relevant one has gauge symmetry U ( N ) 3 with CS levels ( k,k, − 2 k ). The dual geometry is conjectured to be orbifolds AdS$_{4}$ × M 1 , 1 , $^{1}$/$_{Z}$$_{k}$ . A cubic superpotential, with conformal dimension two, is written in terms of the nine bifundamental chiral multipelts. The AdS/CFT duality relation implies that the M-theory spectrum in AdS$_{4}$ × M 1 , 1 , $^{1}$/$_{Z}$$_{k}$ gives the space of gauge singlet operators on the quiver gauge theory side. Instead of try- ing to quantize the supermembrane theory in a curved background, one can study classical membrane solutions and compare the result to field theory operators with large conformal dimensions. This is the strategy advocated first in [8] for AdS$_{5}$ × S $^{5}$, and has been exten- sively used in the study of AdS/CFT relations. Quantitative results for non-supersymmetric solutions lead to very non-trivial checks of the duality between the IIB string background 2