Lie 3-Algebra and Multiple M2-branes

By Pei-Ming Ho, Ru-Chuen Hou, Yutaka Matsuo. 2008

164 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/c2d1cf7faa5a5eacb079b95311a39262b6d906ba

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Citations in the corpus

Constraining Maximally Supersymmetric Membrane Actions (2008, background): “One possibility is to relax the condition that the metric living on the algebra is positive definite and some discussion recently appeared in [16].”
M2-branes, 3-Lie algebras and Plucker relations (2008, background): “The relation of the multiple M2branes theory to the maximally supersymmetric gauge theory which describes multiple D2-branes has been investigated in [8, 9, 10, 11] and some other aspects have been examined in [12, 13, 14, 15].”
M2 to D2 revisited (2008, background): “It was thus conjectured in [8] (see also [15,16]) that there exists no other finite dimensional Lie 3-algebras with a positive definite metric.”
M5 from M2 (2008, background): “When the constraints (1) D is finite and/or (2) h is positive definite are replaced by milder constraints, there are many varieties of 3-algebras which satisfy the fundamental identity (see for example [10, 13]).”
On type IIA Penrose limit and = 6 Chern-Simons theories (2008, background): “If we assume the positive metric of the Lie 3-algebra, the algebra constraints the Lagrangian strongly [14, 18, 19, 20].”
n-ary algebras: a review with applications (2010, methodology): “cubic) matrices has also been explored [174, 231, 232, 56] but again there are difficulties to mimic all properties of Nambu brackets.”
M5-brane in three-form flux and multiple M2-branes (2008, unknown): “(136) In the M5-brane theory with a C-field background, we have δ̂Λ̂b̂µ̇ν̇ = ∂µ̇Λ̂ν̇ − ∂ν̇Λ̂µ̇ + gκ̂λ̇∂λ̇b̂µ̇ν̇ , (137) δ̂Λ̂b̂µµ̇ = ∂µΛ̂µ̇ − ∂µ̇Λ̂µ + gκ̂ν̇∂ν̇ b̂µµ̇ + g(∂µ̇κ̂ν̇)b̂µν̇ .”