Probing non-toric geometry with rotating membranes

Recently Martelli and Sparks presented the first non-toric AdS4/CFT3 duality relation between M-theory on AdS4×V5,2/ZkAdS4×V5,2/Zk and a class of three-dimensional N=2N=2 quiver Chern–Simons-matter theories. V5,2V5,2 is a seven-dimensional homogeneous Sasaki–Einstein manifold with isometry group SO(5)×U(1)RSO(5)×U(1)R, which is in general broken to SU(2)×U(1)×U(1)RSU(2)×U(1)×U(1)R by the orbifold projection if k>1k>1. The dual field theory is described by the A1A1 quiver, U(N)k×U(N)−kU(N)k×U(N)−k gauge group, four bifundamentals, two adjoint chiral multiplets interacting via a cubic superpotential. We explore this proposal by studying various classical membrane solutions moving in V5,2V5,2. Rotating membrane solutions of folded, wrapped, spike, and giant magnon types are presented with their dispersion relations. We also discuss their dual operators in the Chern–Simons-matter theory.