Metric 3-Lie algebras for unitary Bagger-Lambert theories

Understand

We prove a structure theorem for finite-dimensional indefinite-signature metric 3-Lie algebras admitting a maximally isotropic centre.

• This algebraic condition indicates that all the negative-norm states in the associated Bagger-Lambert theory can be consistently decoupled from the physical Hilbert space.
• As an immediate application of the theorem, new examples beyond index 2 are constructed.
• The lagrangian for the Bagger-Lambert theory based on a general physically admissible 3-Lie algebra of this kind is obtained.