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 (6)

• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Modeling Multiple M2's
• Superconformal Chern-Simons Theories
• The M2-M5 Brane System and a Generalized Nahm's Equation
• Selfdual strings and loop space Nahm equations
• Maximally supersymmetric solutions of ten- and eleven-dimensional supergravities

Cited by in corpus (100)

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