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Título

On the Lie-Algebraic Origin of Metric 3-Algebras

AutorMedeiros, Paul de; Figueroa-O'Farrill, José; Méndez-Escobar, E.; Ritter, Patricia
Fecha de publicación26-feb-2009
EditorSpringer
CitaciónCommunications in Mathematical Physics 290(3): 871-902 (2009)
ResumenSince the pioneering work of Bagger-Lambert and Gustavsson, there has been a proliferation of three-dimensional superconformal Chern-Simons theories whose main ingredient is a metric 3-algebra. On the other hand, many of these theories have been shown to allow for a reformulation in terms of standard gauge theory coupled to matter, where the 3-algebra does not appear explicitly. In this paper we reconcile these two sets of results by pointing out the Lie-algebraic origin of some metric 3-algebras, including those which have already appeared in three-dimensional superconformal Chern-Simons theories. More precisely, we show that the real 3-algebras of Cherkis-Samann, which include the metric Lie 3-algebras as a special case, and the hermitian 3-algebras of Bagger-Lambert can be constructed from pairs consisting of a metric real Lie algebra and a faithful (real or complex, respectively) unitary representation. This construction generalises and we will see how to construct many kinds of metric 3-algebras from pairs consisting of a real metric Lie algebra and a faithful (real, complex or quaternionic) unitary representation. In the real case, these 3-algebras are precisely the Cherkis-Samann algebras, which are then completely characterised in terms of this data. In the complex and quaternionic cases, they constitute generalisations of the Bagger-Lambert hermitian 3-algebras and anti-Lie triple systems, respectively, which underlie N = 6 and N = 5 superconformal Chern-Simons theories, respectively. In the process we rederive the relation between certain types of complex 3-algebras and metric Lie superalgebras.
Descripción32 pages.-- Printed version published Sep 2009.-- ArXiv pre-print available at: http://arxiv.org/abs/0809.1086
Versión del editorhttp://dx.doi.org/10.1007/s00220-009-0760-1
URIhttp://hdl.handle.net/10261/16708
DOI10.1007/s00220-009-0760-1
ISSN0010-3616 (Print)
1432-0916 (Online)
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