We classify Lie 3-algebras possessing an invariant lorentzian inner product. The indecomposable objects are either one-dimensional, simple or in one-to-one correspondence with compact real forms of metric semisimple Lie algebras. We analyse the moduli space of classical vacua of the Bagger-Lambert theory corresponding to these Lie 3-algebras. We establish a one-to-one correspondence between one branch of the moduli space and compact riemannian symmetric spaces. We analyse the asymptotic behaviour of the moduli space and identify a large class of models with moduli branches exhibiting the desired N-3/2 behaviour.
- AdS-CFT correspondence