Bagger-Lambert Theory for General Lie Algebras

Abstract

We construct the totally antisymmetric structure constants f^{ABCD} of a 3-algebra with a Lorentzian bi-invariant metric starting from an arbitrary semi-simple Lie algebra. The structure constants f^{ABCD} can be used to write down a maximally superconformal 3d theory that incorporates the expected degrees of freedom of multiple M2 branes, including the "center-of-mass" mode described by free scalar and fermion fields. The gauge field sector reduces to a three dimensional BF term, which underlies the gauge symmetry of the theory. We comment on the issue of unitarity of the quantum theory, which is problematic, despite the fact that the specific form of the interactions prevent the ghost fields from running in the internal lines of any Feynman diagram. Giving an expectation value to one of the scalar fields leads to the maximally supersymmetric 3d Yang-Mills Lagrangian with the addition of two U(1) multiplets, one of them ghost-like, which is decoupled at large g_YM.

12 pages, Latex; small corrections and references added; published version (small typos fixed)

Cited by in corpus (26)

• The complete AdS(4) x CP(3) superspace for the type IIA superstring and D-branes
• Generation of Matrix Models by W-operators
• On the Lie-algebraic origin of metric 3-algebras
• Multiple M2-branes and Generalized 3-Lie algebras
• The fuzzy S^2 structure of M2-M5 systems in ABJM membrane theories
• N=8 superconformal gauge theories and M2 branes
• Towards the Quantum Geometry of the M5-brane in a Constant C-Field from Multiple Membranes
• From N M2's to N D2's
• Scaling limit of N=6 superconformal Chern-Simons theories and Lorentzian Bagger-Lambert theories
• On 3d N=8 Lorentzian BLG theory as a scaling limit of 3d superconformal N=6 ABJM theory
• The Power of the Higgs Mechanism: Higher-Derivative BLG Theories
• Light-cone M5 and multiple M2-branes
• Metric 3-Lie algebras for unitary Bagger-Lambert theories
• A note on Quantum Aspects of Multiple Membranes
• D2 to M2 Procedure for D2-Brane DBI Effective Action
• N=6 Membrane Worldvolume Superalgebra
• Superconformal M2-branes and generalized Jordan triple systems
• Nambu-Lie 3-Algebras on Fuzzy 3-Manifolds
• On non-linear action of multiple M2-branes
• Cohomology of Filippov algebras and an analogue of Whitehead's lemma
• A New Three-Algebra Representation for the {\cal N}=6 su(N)Xsu(N) Superconformal Chern-Simons Theory
• Abelian Vortex in Bagger-Lambert-Gustavsson Theory
• Aspects of U-duality in BLG models with Lorentzian metric 3-algebras
• Remark About Scaling Limit of ABJ Theory
• 3d CFT and Multi M2-brane Theory on RxS^2
• Membranes, Strings and Integrability