具有Lorentz度量3-代数的BLG模型的U-对偶性质
Aspects of U-duality in BLG models with Lorentzian metric 3-algebras
摘要：
在我们以前的文章中，我们证明了基于Lorentzian度量3-代数的BLG模型给出了Dp-膜作用量，其世界体积在环面T^d（d=p-2）上是紧化的.这里的3-代数是一个广义的一个d+1对洛伦兹度量生成元，并表示为一个循环代数的中心扩张。本文导出了与洛伦兹度规生成元有关的超杨-米尔斯场的耦合常数、T^d模和某些R-R通量与鬼场的VEV之间的精确关系。特别地，当d=1时，我们导出了带θ项的Yang-Mills作用量，并证明了SL（2，Z）Montonen-Olive对偶性是通过两个VEV的旋转来实现的。此外，还将NS-NS 2型通量等模参数确定为3-代数的形变参数。通过结合它们，我们恢复了U-对偶对称性所需的大部分模参数。
英文摘要：
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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