Affine Kac-Moody algebras, CHL strings and the classification of tops
Affine Kac-Moody algebras, CHL strings and the classification of tops
复制标题
仿射 Kac-Moody 代数、CHL 弦和陀螺分类
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
H. Skarke
中科院分区：
文献类型：
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作者：
V. Bouchard;H. Skarke
Candelas和Font引入了“顶”的概念，作为三维自反多面体的一半，并注意到弦理论中增强规范群的Dynkin图可以从它们中读出。我们将所有满足广义定义的顶点分类为一个包含原点的小平面和距离原点1的其他小平面的晶格多面体。这些物体对椭圆纤维化退化的局部几何形状进行了历史编码。我们给出了一个处方分配一个仿射，可能扭曲的卡茨-穆迪代数的任何这样的顶部（更一般的任何椭圆纤维化结构）在一个精确的方式，涉及到简单的根的长度和系数的零根。与扭曲Kac-Moody代数相关的拓扑可以用来构造规范群降秩的弦紧化。
Candelas and Font introduced the notion of a `top' as half of a three dimensional reflexive polytope and noticed that Dynkin diagrams of enhanced gauge groups in string theory can be read off from them. We classify all tops satisfying a generalized definition as a lattice polytope with one facet containing the origin and the other facets at distance one from the origin. These objects torically encode the local geometry of a degeneration of an elliptic fibration. We give a prescription for assigning an affine, possibly twisted Kac-Moody algebra to any such top (and more generally to any elliptic fibration structure) in a precise way that involves the lengths of simple roots and the coefficients of null roots. Tops related to twisted Kac-Moody algebras can be used to construct string compactifications with reduced rank of the gauge group.