Multiple Membranes in M-theory

TL;DR

This paper reviews the development of multiple membrane theories in M-theory, focusing on 3-algebra formulations, their relation to superconformal Chern-Simons theories, and implications for gauge/gravity duality and M-brane physics.

Contribution

It introduces 3-algebra based models for multiple membranes, connecting them to superconformal Chern-Simons theories and exploring their physical and duality properties.

Findings

Identification of models with M2-branes in Z_k orbifolds

Establishment of AdS_4/CFT_3 correspondence for these models

Discussion of mass deformations and higher derivative corrections

Abstract

We review developments in the theory of multiple, parallel membranes in M-theory. After discussing the inherent difficulties pertaining to a maximally supersymmetric lagrangian formulation with the appropriate field content and symmetries, we discuss how introducing the concept of 3-algebras allows 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 describe how these are equivalent to a type of conventional superconformal Chern-Simons gauge theories at level k, coupled to bifundamental matter. Analysing the physical properties of these theories leads to the identification of a certain subclass of models with configurations of M2-branes in Z_k orbifolds of M-theory. In addition these models give rise to a whole new sector of the gauge/gravity duality in the form of an AdS_4/CFT_3 correspondence. We also discuss mass deformations, higher derivative corrections as well as the possibility of extracting information about M5-brane physics.