This paper reviews the properties and applications of certain n-ary generalizations of Lie
algebras in a self-contained and unified way. These generalizations are algebraic structures …

We review developments in the theory of multiple, parallel membranes in M-theory. After
discussing the inherent difficulties with constructing a maximally supersymmetric lagrangian …

We extend the Script N= 4 superconformal Chern-Simons theories of Gaiotto and Witten to
those with additional twisted hyper-multiplets. The new theories are generically linear quiver …

We derive the general form for a three-dimensional scale-invariant field theory with N= 6
supersymmetry, SU (4) R-symmetry and a U (1) global symmetry. The results can be written …

We give two independent arguments why the classical membrane fields should be take
values in a loop algebra. The first argument comes from how we may construct selfdual …

Abstract Recently, Aharony, Bergman, Jafferis and Maldacena proposed that the Script N= 6
Chern-Simons gauge theories are holographically dual to the M-theory backgrounds with …

We find that the structure constants 4-form of a metric 3-Lie algebra is the sum of the volume
forms of orthogonal 4-planes proving a conjecture in math/0211170. In particular, there is no …

Recently an action based on Lie 3-algebras was proposed to describe M2-branes. We study
the case of infinite dimensional Lie 3-algebras based on the Nambu-Poisson structure of …

We present two derivations of the multiple D2 action from the multiple M2-brane model
proposed by Bagger-Lambert and Gustavsson. The first one is to start from Lie 3-algebra …

Motivated by the recent proposal of an N= 8 supersymmetric action for multiple M2-branes,
we study the Lie 3-algebra in detail. In particular, we focus on the fundamental identity and …