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arXiv · 0902.4674

Metric 3-Lie algebras for unitary Bagger-Lambert theories

Paul de Medeiros·José Figueroa-O'Farrill·Elena Méndez-Escobar·Patricia Ritter
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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.

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Paul de Medeiros, José Figueroa-O'Farrill, Elena Méndez-Escobar, Patricia Ritter. 2009-02-26. Metric 3-Lie algebras for unitary Bagger-Lambert theories. https://doi.org/10.1088/1126-6708%2F2009%2F04%2F037

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