M2-branes, 3-Lie Algebras and Plucker relations

Details M2-branes, 3-Lie Algebras and Plucker relations M2-branes, 3-Lie Algebras and Plucker relations

2008-04-16

arxiv.org/abs/0804.2662v3

JHEP 0805:054,2008

Physics

High Energy Physics

High Energy Physics - Theory

8 pages, minor changes, published version

Scientific paper

10.1088/1126-6708/2008/05/054

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 metric 3-Lie algebra associated to a $\mathfrak{u}(N)$ Lie algebra for $N>2$. We examine the implication of this result on the existence of a multiple M2-brane theory based on metric 3-Lie algebras.

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