and N = 4 super-Yang-Mills theory in four dimensions. For a review of related works, we refer the readers to [9–11]. The energy and angular momenta of the membrane theory correspond to the conformal dimension and global charges on the field theory side, respectively. We will consider various spinning membranes in AdS$_{4}$ × M 1 , 1 , 1 background, and when the energy becomes large, they are expected to give the conformal dimension of very long operators. Membranes rotating in AdS$_{7}$ × S 4 are studied in [12]. It is also extended to AdS$_{4}$ × S $^{7}$, AdS$_{4}$ × Q 1 , 1 , 1 and various warped backgrounds in [13, 14]. More papers devoted to exact membrane solutions in AdS$_{4}$ × S 7 or the IIA background AdS$_{4}$ ×$_{CP}$ 3 can be found in [15, 16]. In order to concentrate on the novelty of the new duality pair, we will consider membranes moving entirely in M 1 , 1 , $^{1}$. Since the seven-dimensional internal space is described by the scalar fields via duality, the rotating membranes then correspond to pure-scalar operators. The data of angular momenta help us identifying the dual operators, and the energy tells us how big is the anomalous dimension. This article is organized as follows. In Sec. II, we review the duality proposal for AdS$_{4}$ × M 1 , 1 , $^{1}$/$_{Z}$$_{k}$ and discuss the identification of supersymmetric operators and Kaluza- Klein modes. In Sec. III we present the gauge fixed membrane action, mainly to setup the notation. In Sec. IV A we consider particle-like solutions and discuss their identification as BPS operators. Sec. IV B is the main part where we present explicit multi-spin membrane solutions and discuss their field theory duals. We conclude in Sec. V. Let us start by presenting the 11 dimensional background AdS$_{4}$ × M 1 , 1 , 1 , which preserves 1 $_{4}$-supersymmetry. The metric is given as follows, As a configuration of 11 dimensional supergravity, the solution carries 4-form field strength over Vol( AdS$_{4}$ ). But for the specific type of membrane solutions we will consider, we can 3 II. M-THEORY ON AdS$_{4}$ × M 1 , 1 , 1 AND ITS CHERN-SIMONS DUAL ds 2 = ds 2 AdS$_{4}$ + ds 2 M 1 , 1 , 1 , (1) ds 2 AdS$_{4}$ = L 2 $^{(}$− cosh $^{2}$ρ dt 2 + dρ 2 + sinh $^{2}$ρ ( dϑ 2 + sin $^{2}$ϑdϕ$^{2}$) ) , (2) ds 2 M 1 , 1 , 1 = L 2 $_{64}$[ dψ + 3 sin $^{2}$µ ( d ˜ ψ + cos ˜ θd ˜ φ ) + 2 cos θdφ ] 2 + L 2 8 ( dθ 2 + sin $^{2}$θdφ$^{2}$) + 3 L 2 4 [ dµ 2 + 1 4 sin $^{2}$µ ( d ˜ θ 2 + sin 2 ˜ θd ˜ φ 2 + cos $^{2}$µ ( d ˜ ψ + cos ˜ θd ˜ φ ) $^{2}$)] . (3)