Strong homotopy lie algebras, generalized nahm equations and multiple M2-branes

Calin Lazaroiu, Daniel McNamee, Christian Saemann, Aleksandar Zejak

Research output: Working paper

Abstract

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.
Original languageEnglish
Publication statusPublished - 26 Jan 2009

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