Strong Homotopy Lie Algebras, Generalized Nahm Equations and Multiple M2-branes

Details Strong Homotopy Lie Algebras, Generalized Nahm Equations and Multiple M2-branes Strong Homotopy Lie Algebras, Generalized Nahm Equations and Multiple M2-branes

2009-01-26

arxiv.org/abs/0901.3905v1

Physics

High Energy Physics

High Energy Physics - Theory

1+28 pages

Scientific paper

We review various generalizations of the notion of Lie algebras, in particular those appearing in the recently proposed Bagger-Lambert-Gustavsson model, and study their interrelations. We find that Filippov's n-Lie algebras are a special case of strong homotopy Lie algebras. Furthermore, we define a class of homotopy Maurer-Cartan equations, which contains both the Nahm and the Basu-Harvey equations as special cases. Finally, we show how the super Yang-Mills equations describing a Dp-brane and the Bagger-Lambert-Gustavsson equations supposedly describing M2-branes can be rewritten as homotopy Maurer-Cartan equations, as well.

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