Lorentzian Lie 3-algebras and their Bagger-Lambert moduli space
arXiv:0805.4363 · doi:10.1088/1126-6708/2008/07/111
Abstract
We classify Lie 3-algebras possessing an invariant lorentzian inner product. The indecomposable objects are in one-to-one correspondence with compact real forms of metric semisimple Lie algebras. We analyse the moduli space of classical vacua of the Bagger-Lambert theory corresponding to these Lie 3-algebras. We establish a one-to-one correspondence between one branch of the moduli space and compact riemannian symmetric spaces. We analyse the asymptotic behaviour of the moduli space and identify a large class of models with moduli branches exhibiting the desired N^{3/2} behaviour.
25 pages, 2 figures. V2: some minor cosmetic changes, several references added, a misattribution corrected, acknowledgments now included, and the authors now listed in the correct English lexicographic order; V3: typos corrected and reference added
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