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Metric Lie 3-algebras in Bagger-Lambert theory

De Medeiros, Paul F., Figueroa-O'Farrill, José and Méndez-Escobar, Elena 2008. Metric Lie 3-algebras in Bagger-Lambert theory. Journal of High Energy Physics 2008 (08) , 045. 10.1088/1126-6708/2008/08/045

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We recast physical properties of the Bagger-Lambert theory, such as shift-symmetry and decoupling of ghosts, the absence of scale and parity invariance, in Lie 3-algebraic terms, thus motivating the study of metric Lie 3-algebras and their Lie algebras of derivations. We prove a structure theorem for metric Lie 3-algebras in arbitrary signature showing that they can be constructed out of the simple and one-dimensional Lie 3-algebras iterating two constructions: orthogonal direct sum and a new construction called a double extension, by analogy with the similar construction for Lie algebras. We classify metric Lie 3-algebras of signature (2, p) and study their Lie algebras of derivations, including those which preserve the conformal class of the inner product. We revisit the 3-algebraic criteria spelt out at the start of the paper and select those algebras with signature (2, p) which satisfy them, as well as indicate the construction of more general metric Lie 3-algebras satisfying the ghost-decoupling criterion.

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

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