Multiple Membranes in M-theory

We review developments in the theory of multiple, parallel membranes in M-theory. After discussing the inherent difficulties with constructing a maximally supersymmetric lagrangian with the appropriate field content and symmetries, we introduce 3-algebras and show how they allow for such a description. Different choices of 3-algebras lead to distinct classes of 2+1 dimensional theories with varying degrees of supersymmetry. We then demonstrate that these theories are equivalent to conventional superconformal Chern–Simons gauge theories at level k, but with bifundamental matter. Analysing the physical properties of these theories leads to the identification of a certain subclass of models with configurations of M2-branes on Zk orbifolds. These models give rise to a whole new gauge/gravity duality in the form of an AdS4/CFT3 correspondence. We also discuss mass deformations, higher derivative corrections, and the possibility of extracting information about M5-brane physics.