Lie 3-Algebra and Multiple M2-branes

Abstract

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 the relation with Nambu-Poisson bracket. Some new algebras not known in the literature are found. Next we consider cubic matrix representations of Lie 3-algebras. We show how to obtain higher dimensional representations by tensor products for a generic 3-algebra. A criterion of reducibility is presented. We also discuss the application of Lie 3-algebra to the membrane physics, including the Basu-Harvey equation and the Bagger-Lambert model.

28 pages

References in corpus (8)

• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Modeling Multiple M2's
• Comments on Multiple M2-branes
• Selfdual strings and loop space Nahm equations
• N = 8 Superconformal Chern--Simons Theories
• M2-branes on M-folds
• M-theory branes and their interactions
• A toy model of open membrane field theory in constant 3-form flux

Cited by in corpus (22)

• The SU(2) x SU(2) sector in the string dual of N=6 superconformal Chern-Simons theory
• Multiple M2-branes and Generalized 3-Lie algebras
• Mass-Deformed Bagger-Lambert Theory and its BPS Objects
• From N M2's to N D2's
• Scaling limit of N=6 superconformal Chern-Simons theories and Lorentzian Bagger-Lambert theories
• Nijenhuis operators on $n$-Lie algebras
• Topological branes, p-algebras and generalized Nahm equations
• Quantized Nambu-Poisson Manifolds and n-Lie Algebras
• Symplectic, product and complex structures on 3-Lie algebras
• A note on Quantum Aspects of Multiple Membranes
• Nambu bracket and M-theory
• A new approach to representations of $3$-Lie algebras and abelian extensions
• D2 to M2 Procedure for D2-Brane DBI Effective Action
• Nambu Bracket for M Theory
• Triality and Bagger-Lambert Theory
• The birth of the universe in a new G-Theory approach
• 3-Lie bialgebras and 3-Lie classical Yang-Baxter equations in low dimensions
• Gauge Fields, Membranes and Subdeterminant Vector Models
• Classification of $(n+3)$-dimensional metric $n$-Lie algebras
• Deformations and extensions of modified $\lambda$-differential $3$-Lie Algebras
• Quadratic and symplectic structures on 3-(Hom)-$\rho$-Lie algebras
• Extension of Malcev algebra and applications to gravity