ADHM多面体
ADHM Polytopes
摘要：
本文讨论了四维正多面体对称性下Yang-Mills瞬子的ADHM数据的构造。我们表明，可以使用一个简单的修改以前开发的柏拉图数据的方法进行研究的情况下，五位体。对于剩余的多面体，我们描述了一个框架，其中的ADHM数据的构建块对应于扩展Dynkin图中的边，通过麦凯对应关系产生。这些积木，然后组装成ADHM数据，通过识别对相关的二元多面体群的交换表示。我们说明了我们的程序的建设ADHM数据与五体，超八面体和24细胞，与瞬子电荷分别为4，7和23。此外，我们表明，在我们的框架内，这些都是最低的可能收费与这些对称性。拓扑电荷密度图证实了多面体结构，并阐明了与JNR瞬子数据的关系。
英文摘要：
We discuss the construction of ADHM data for Yang-Mills instantons with the symmetries of the regular polytopes in four dimensions. We show that the case of the pentatope can be studied using a simple modification of the approach previously developed for platonic data. For the remaining polytopes, we describe a framework in which the building blocks of the ADHM data correspond to the edges in the extended Dynkin diagram that arises via the McKay correspondence. These building blocks are then assembled into ADHM data through the identification of pairs of commuting representations of the associated binary polyhedral group. We illustrate our procedure by the construction of ADHM data associated with the pentatope, the hyperoctahedron and the 24-cell, with instanton charges 4, 7 and 23, respectively. Furthermore, we show that within our framework these are the lowest possible charges with these symmetries. Plots of topological charge densities are presented that confirm the polytope structure and the relation to JNR instanton data is clarified.
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