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arXiv · 0804.2110

Lie 3-Algebra and Multiple M2-branes

Pei-Ming Ho·Ru-Chuen Hou·Yutaka Matsuo
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Abstract

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.

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Pei-Ming Ho, Ru-Chuen Hou, Yutaka Matsuo. 2008-04-23. Lie 3-Algebra and Multiple M2-branes. https://doi.org/10.1088/1126-6708%2F2008%2F06%2F020

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