K3表面上IIA型弦论的量子霍尔效应工程
Engineering of Quantum Hall Effect from Type IIA String Theory on The K3 Surface
摘要：
利用K ~ 3面上的D-膜组态，给出了1+2维量子霍尔效应（QHE）的六维IIA型弦实现.基于K3霍奇钻石的垂直和水平线，我们设计了两种不同的弦实现。垂直线代表了一个用D2和D 6-膜包裹K3曲面的实现。水平的一个与层次弦描述相关，该描述是从一个生活在一堆D4-膜上的D4-规范规范理论获得的，这些D4-膜包裹着嵌入在具有变形奇点的K3表面中的相交2-球。这些几何可按三类卡茨-穆迪代数分类：普通几何，即有限维几何，仿射几何和不定几何。我们发现，在1+2维空间中，在以仿射Dynkin图形式排列的相交2-球面上的量子规范理论中，不可能出现弦QHE。QHE的严格实现只能对有限和不确定几何进行。特别地，有限李代数给出具有分数填充分数的模型，而不确定李代数将具有负填充分数的模型分类，这可以与石墨烯中的孔的物理学相关联。
英文摘要：
Using D-brane configurations on the K3 surface, we give six dimensional type IIA stringy realizations of the Quantum Hall Effect (QHE) in 1+2 dimensions. Based on the vertical and horizontal lines of the K3 Hodge diamond, we engineer two different stringy realizations. The vertical line presents a realization in terms of D2 and D6-branes wrapping the K3 surface. The horizontal one is associated with hierarchical stringy descriptions obtained from a quiver gauge theory living on a stack of D4-branes wrapping intersecting 2-spheres embedded in the K3 surface with deformed singularities. These geometries are classified by three kinds of the Kac-Moody algebras: ordinary, i.e finite dimensional, affine and indefinite. We find that no stringy QHE in 1+2 dimensions can occur in the quiver gauge theory living on intersecting 2-spheres arranged as affine Dynkin diagrams. Stringy realizations of QHE can be done only for the finite and indefinite geometries. In particular, the finite Lie algebras give models with fractional filling fractions, while the indefinite ones classify models with negative filling fractions which can be associated with the physics of holes in the graphene.
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