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Metric 3-Lie algebras for unitary Bagger-Lambert theories

De Medeiros, Paul F., Figueroa-O'Farrill, José, Méndez-Escobar, Elena and Ritter, Patricia 2009. Metric 3-Lie algebras for unitary Bagger-Lambert theories. Journal of High Energy Physics 2009 (04) , 037. 10.1088/1126-6708/2009/04/037

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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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Uncontrolled Keywords: M-Theory; AdS-CFT and dS-CFT Correspondence
Publisher: IOP Science
ISSN: 1029-8479
Last Modified: 19 Mar 2016 23:07

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