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M2-branes, 3-Lie Algebras and Plucker relations · Around

2008

M2-branes, 3-Lie Algebras and Plucker relations

Papadopoulos, G.

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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.

Built on

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M. Mimura and H. Toda, “Topology of Lie Groups, I and II,” American Mathematical Society Vol 91, (1991)
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J. Figueroa-O’Farrill and G. Papadopoulos, “Pluecker-type relations for orthogonal planes,” arXiv:math/0211170
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Then

J. Bagger and N. Lambert, “Modeling multiple M2’s,” Phys. Rev. D 75
2007
Later among the works it cites.
J. Bagger and N. Lambert, “Gauge Symmetry and Supersymmetry of Multiple M2-Branes,” Phys. Rev. D 77
Original
2008
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