M2-branes, 3-Lie Algebras and Plucker relations

Abstract

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.

8 pages, minor changes, published version

References in corpus (2)

• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Modeling Multiple M2's

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