Strong Homotopy Lie Algebras, Generalized Nahm Equations and Multiple M2-branes
arXiv:0901.3905
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.
1+28 pages
References in corpus (7)
- Gauge Symmetry and Supersymmetry of Multiple M2-Branes
- Algebraic structures on parallel M2-branes
- Comments on the Bagger-Lambert theory and multiple M2-branes
- Multiple M2-branes and Generalized 3-Lie algebras
- Higher Yang-Mills Theory
- On Superspace Actions for Multiple M2-Branes, Metric 3-Algebras and their Classification
- Formal Maurer-Cartan Structures: from CFT to Classical Field Equations