Multiple Membranes in M-theory

TL;DR

The article surveys the development of field theories for multiple M2-branes, beginning with 11D supergravity and M-branes, and advancing through the Bagger–Lambert–Gustavsson (BLG) and Aharony–Bergman–Jafferis–Maldacena (ABJM) frameworks grounded in 3-algebras and Chern-Simons-matter theories. It details how 3-algebras underpin maximally supersymmetric 2+1D theories, how ABJM realizes N=6 CS-matter theories with U(n)×U(n) gauge groups describing M2-branes at a C^4/Z_k orbifold, and how these theories exhibit AdS_4/CFT_3 duality with AdS_4×S^7/ Z_k (and its IIA limit for large k). The text further develops the vacuum moduli spaces, a novel Higgs mechanism linking ABJM/BLG to 3D Yang–Mills, and the role of monopole/'t Hooft operators in encoding 11D momentum and dualities, including ABJ/discrete torsion generalizations. Collectively, the work elucidates how membrane dynamics are captured by CS-matter theories, their gravity duals, and the nonperturbative structures that connect M-theory to string theory.

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.

Figures (3)

• Figure 1: The D3-brane segments can move independently.
• Figure 2: Introduction of D5's and mass deformation.
• Figure 3: a) A simple quiver from Gaiotto-Witten theory with hypermultiplets. The gauge groups can be $G_1=\mathrm{U}(n_1)$, $G_2=\mathrm{U}(n_2)$ or $G_1=\mathrm{Sp}(n_1)$, $G_2=\mathrm{SO}(n_2)$. b) A longer quiver from a theory containing both hyper and twisted hypermultiplets. The gauge groups can be $G_i=\mathrm{U}(n_i)$, $G_j=\mathrm{U}(n_j)$ or $G_i=\mathrm{Sp}(n_i)$, $G_{i+1}=\mathrm{SO}(n_{i+1})$. The quiver can also be closed into a circle.