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arXiv · 0901.2003

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

Pei-Ming Ho·Yutaka Matsuo·Shotaro Shiba
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Abstract

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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Pei-Ming Ho, Yutaka Matsuo, Shotaro Shiba. 2009-01-28. Lorentzian Lie (3-)algebra and toroidal compactification of M/string theory. https://doi.org/10.1088/1126-6708%2F2009%2F03%2F045

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