On the Moduli Space of Elliptic Maxwell-Chern-Simons Theories
On the Moduli Space of Elliptic Maxwell-Chern-Simons Theories
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DOI：
10.1143/ptp.120.509
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发表时间：
2008-06
影响因子：
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通讯作者：
Y. Imamura;Keisuke Kimura
中科院分区：
文献类型：
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作者：
Y. Imamura;Keisuke Kimura
对于4维椭圆模型，我们分析了用圆箭图描述的三维N=3 Maxwell-Chern-Simons理论的低能极限的模空间。我们用D3-NS5-(k，1)5膜系定义了具有任意五膜数的理论。在低能极限下，超对称性有望增强到N=4i。我们证明了Higgs分支是C4的阿贝尔分支，其中所有的双基标量场都有真空期望值。我们证实得到了与膜系的M-理论对偶相同的几何结构。我们还考虑了通过引入两种以上五膜而实现的理论，得到了作为模空间的非环面四重空间。近年来，三维超共形场理论作为描述不同背景下多个M2膜的理论引起了人们的极大兴趣。这是由巴格尔和兰伯特以及古斯塔夫森提出的一类新的三维理论引发的。4)，5)模型(BLG模型)具有N(d=3)=8的超共形对称性，且基于Lie 3-代数。BLG模型的作用包括决定相互作用形式的Lie 3-代数的结构常数f abc d和出现在动力学项系数中的度规Hab。这些张量必须满足作用量的超对称不变性所要求的某些条件。如果这些张量满足条件，我们就可以写下BLG模型的作用。对结构常数施加的约束称为基本恒等式。人们很快意识到这个恒等式是非常有限制性的，6)并且证明了如果我们假设度量是正定的，并且代数是有限维的，那么只有一个非平凡的李3-代数，7)，8)，称为A4代数。基于A4代数的BLG模型是一个SU(2)×SU(2)Chern-Simons理论，每个SU(2)因子有k能级和−k能级。对该模型的分析表明，该模型描述了一对处于特定背景下的M2膜。9)-11)作为一个关于任意多个M2膜的理论，文献[1]提出了一个基于洛伦兹度量的代数模型。12)-14)。由于不确定度规，该模型包含了不需要的鬼模。尽管鬼模可以通过将它们视为满足经典运动方程的背景场来消除，或者通过测量某些对称性并固定它们，16)，17)，这个过程打破了共形不变性，该理论通过文献[4)，16)，18)提出的机制成为D2-膜理论。19)除非
We analyze the moduli space of the low-energy limit of 3-dimensional N = 3 MaxwellChern-Simons theories described by circular quiver diagrams, as for 4-dimensional elliptic models. We define the theories by using D3-NS5-(k,1)5-brane systems with an arbitrary number of fivebranes. The supersymmetry is expected to be enhanced to N =4i n the low-energy limit. We show that the Higgs branch, in which all bifundamental scalar fields develop vacuum expectation values, is an abelian orbifold of C 4 . We confirm that the same geometry is obtained as an M-theory dual of the brane system. We also consider theories realized by introducing more than two kinds of fivebranes, and obtain nontoric fourfolds as moduli spaces. Recently, there has been great interest in 3-dimensional superconformal field theories as theories for describing multiple M2-branes in various backgrounds. This was triggered by the proposal of a new class of 3-dimensional theories by Bagger and Lambert, 1)–3) and Gusstavson. 4),5) The model (BLG model) possesses N(d=3) =8 superconformal symmetry and is based on Lie 3-algebra. The action of the BLG model includes the structure constant f abc d of a Lie 3-algebra, which determines the form of the interactions, and a metric h ab , which appears in the coefficients of the kinetic terms. These tensors must satisfy certain conditions required by the supersymmetry invariance of the action. If these tensors satisfy the conditions, we can write down the action of a BLG model. The constraint imposed on the structure constant is called a fundamental identity. It was soon realized that the identity is very restrictive, 6) and it was proved that if we assume that the metric is positive definite and the algebra is finite dimensional, there is only one nontrivial Lie 3-algebra, 7),8) which is called an A4 algebra. The BLG model based on the A4 algebra is a SU(2)×SU(2) Chern-Simons theory with levels k and −k for each SU(2) factor. Analysis of this model showed that it describes a pair of M2-branes in certain orbifold backgrounds. 9)–11) As a theory for an arbitrary number of M2-branes, a model based on an algebra with a Lorenzian metric was proposed in Refs. 12)– 14). Because of the indefinite metric, the model includes unwanted ghost modes. Although the ghost modes can be removed by treating them as background fields satisfying classical equations of motion, 14),15) or by gauging certain symmetries and fixing them, 16),17) this procedure breaks the conformal invariance, and the theory becomes D2-brane theory 14),16),18) by the mechanism proposed in Ref. 19) unless the