Lorentzian Lie (3-)algebra and toroidal compactification of M/string theory

Details Lorentzian Lie (3-)algebra and toroidal compactification of M/string theory Lorentzian Lie (3-)algebra and toroidal compactification of M/string theory

2009-01-14

arxiv.org/abs/0901.2003v2

Physics

High Energy Physics

High Energy Physics - Theory

39 pages; v2: minor corrections, reference added

Scientific paper

10.1088/1126-6708/2009/03/045

We construct a class of Lie 3-algebras with an arbitrary number of pairs of generators with Lorentzian signature metric. Some examples are given and corresponding BLG models are studied. We show that such a system in general describes a supersymmetric massive vector multiplets after the ghost fields are Higgsed. Simple systems with nontrivial interaction are realized by infinite dimensional Lie 3-algebras associated with the loop algebras. The massive fields are then naturally identified with the Kaluza-Klein modes by the toroidal compactification triggered by the ghost fields. For example, Dp-brane with an (infinite dimensional) affine Lie algebra symmetry $\hat g$ can be identified with D(p+1)-brane with gauge symmetry $g$.

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