基于复曲面几何的弦论分数量子Hall填充因子
Fractional Quantum Hall Filling Factors from String Theory using Toric Geometry
摘要：
利用复曲面Cartan矩阵作为阿贝尔规范荷，提出了一类弦分数量子霍尔效应，并给出了最近实验观测到的填充因子值.更准确地说，我们从紧化在四个复维超凯勒流形X上的M理论中导出了相应的陈-西蒙斯型模型^[4]。这些流形被看作是一个特殊的N=4的二维西格玛模型的目标空间，根据复曲面Cartan矩阵，它们可以用相交的二维复曲面簇Vi ^2上的余切丛来标识。探索弦对偶的结果，本文提出的双曲对称性可以由缠绕在这类相交环面簇上的D 6-斑与R-R规范场相互作用得到。这个弦论实现提供了一个几何解释的填充因子的复曲面和欧拉特征拓扑数据的紧化几何。具体地说，建立了双层膜的显式模型。
英文摘要：
Using toric Cartan matrices as abelian gauge charges, we present a class of stringy fractional quantum Hall effect (FQHE) producing some recent experimental observed filling factor values. More precisely, we derive the corresponding Chern-Simons type models from M-theory compactified on four complex dimensional hyper-Kähler manifolds X^4. These manifolds, which are viewed as target spaces of a particular N=4 sigma model in two dimensions, are identified with the cotangent bundles over intersecting 2-dimensional toric varieties V_i^2 according to toric Cartan matrices. Exploring results of string dualities, the presented FQHE can be obtained from D6-banes wrapping on such intersecting toric varieties interacting with R-R gauge fields. This string theory realization provides a geometric interpretation of the filling factors in terms of toric and Euler characteristic topological data of the compactified geometry. Concretely, explicit bilayer models are worked out in some details.
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