Aspects of U-duality in BLG models with Lorentzian metric 3-algebras

Details Aspects of U-duality in BLG models with Lorentzian metric 3-algebras Aspects of U-duality in BLG models with Lorentzian metric 3-algebras

2009-05-11

arxiv.org/abs/0905.1445v2

JHEP 0906:053,2009

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, v2: minor corrections

Scientific paper

10.1088/1126-6708/2009/06/053

In our previous paper, it was shown that BLG model based on a Lorentzian metric 3-algebra gives Dp-brane action whose worldvolume is compactified on torus T^d (d=p-2). Here the 3-algebra was a generalized one with d+1 pairs of Lorentzian metric generators and expressed in terms of a loop algebra with central extensions. In this paper, we derive the precise relation between the coupling constant of the super Yang-Mills, the moduli of T^d and some R-R flux with VEV's of ghost fields associated with Lorentzian metric generators. In particular, for d=1, we derive the Yang-Mills action with theta term and show that SL(2,Z) Montonen-Olive duality is realized as the rotation of two VEV's. Furthermore, some moduli parameters such as NS-NS 2-form flux are identified as the deformation parameters of the 3-algebras. By combining them, we recover most of the moduli parameters which are required by U-duality symmetry.

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