We discuss a couple of topics motivated by the Chern-Simons type gauge theory description of M2-branes in nontrivial backgrounds. In the first part we start by briefly reviewing the 3-algebra construction of Bagger, Lambert and Gustavsson. Then we propose an orbifold truncation prescription of 3-algebra, and show how one can 'derive' the ABJM model through matrix regularization. In the second part, we report on some explicit classical solutions of rotating membranes in Sasaki-Einstein 7-manifold M(111). We discuss the dual operators on the CS side, for several different class of spinning membranes.

The study of supersymmetric solutions in supergravity have provided invaluable insight into quantum gravity via AdS/CFT correspondence. In this talk I present a new class of intriguing Kahler geometry which appears in the study of AdS solutions from D3 and M2-branes wrapped on 2-cycles. Solving the master equation, which has higher-order couplings in Ricci tensor, we obtain new AdS solutions.

We discuss a couple of topics motivated by the Chern-Simons type gauge theory description of M2-branes in nontrivial backgrounds. In the first part we start by briefly reviewing the 3-algebra construction of Bagger, Lambert and Gustavsson. Then we propose an orbifold truncation prescription of 3-algebra, and show how one can 'derive' the ABJM model through matrix regularization. In the second part, we report on some explicit classical solutions of rotating membranes in Sasaki-Einstein 7-manifold M(111). We discuss the dual operators on the CS side, for several different class of spinning membranes.