对偶级联与仿射Weyl群
Duality Cascades and Affine Weyl Groups
摘要：
环状膜结构允许Hanany-Witten跃迁的后续应用，这被称为对偶级联。通过研究具有Weyl群对称性的量子曲线对应的对偶级联过程，发现了仿射Weyl群的一个隐藏结构。也就是说，由所有最终目的地组成的对偶级联的基本域由仿射Weyl腔表征，并且对偶级联被实现为仿射Weyl群的平移，其中膜配置中的总秩与仿射代数的分级算子相关联。仿射Weyl群的结构保证了过程的有限性和对偶级联端点的唯一性。除了原来的对偶级联，我们可以推广到Fayet-Iliopoulos参数的情况。在那里我们可以利用Weyl群来类似地分析基本域，并且发现基本域仍然是仿射Weyl腔。我们进一步解释外尔群，我们强加的Hanany-Witten过渡的“一半”。
英文摘要：
Brane configurations in a circle allow subsequent applications of the Hanany-Witten transitions, which are known as duality cascades. By studying the process of duality cascades corresponding to quantum curves with symmetries of Weyl groups, we find a hidden structure of affine Weyl groups. Namely, the fundamental domain of duality cascades consisting of all the final destinations is characterized by the affine Weyl chamber and the duality cascades are realized as translations of the affine Weyl group, where the overall rank in the brane configuration associates to the grading operator of the affine algebra. The structure of the affine Weyl group guarantees the finiteness of the processes and the uniqueness of the endpoint of the duality cascades. In addition to the original duality cascades, we can generalize to the cases with Fayet-Iliopoulos parameters. There we can utilize the Weyl group to analyze the fundamental domain similarly and find that the fundamental domain continues to be the affine Weyl chamber. We further interpret the Weyl group we impose as a "half" of the Hanany-Witten transition.
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