Metric 3-Lie algebras for unitary Bagger-Lambert theories

Abstract

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. Following an expansion around a suitable vacuum, the precise relationship between such theories and certain more conventional maximally supersymmetric gauge theories is found. These typically involve particular combinations of N=8 super Yang-Mills and massive vector supermultiplets. A dictionary between the 3-Lie algebraic data and the physical parameters in the resulting gauge theories will thereby be provided.

38 pages

References in corpus (8)

• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Modeling Multiple M2's
• M2 to D2
• Membranes on an Orbifold
• M2-branes, 3-Lie Algebras and Plucker relations
• Bagger-Lambert Theory for General Lie Algebras
• N=8 superconformal gauge theories and M2 branes

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• A class of hermitian generalized Jordan triple systems and Chern-Simons gauge theory