Superconformal block quivers, duality trees and Diophantine equations
Superconformal block quivers, duality trees and Diophantine equations
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DOI：
10.1007/jhep11(2013)017
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发表时间：
2012-11
影响因子：
5.4
通讯作者：
A. Hanany;Yang-Hui He;Chuang Sun;Spyros Sypsas
中科院分区：
文献类型：
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作者：
A. Hanany;Yang-Hui He;Chuang Sun;Spyros Sypsas
我们推广了前人关于=1，(3+1)维超共形块箭图规范理论的结果。众所周知，一个理论成为超共形的必要条件，即除了异常消除外，贝塔函数和伽马函数也消失了，根据箭图数据转化为丢番图方程。我们重新推导了低块数的结果，揭示了这类理论的一类可能的超共形不动点背后的一种新的有趣的代数结构。在显式地计算了五块情况下的丢番图方程后，我们使用这种结构将结果重新组织成一种可以应用于任意块数的形式。我们认为这些理论可以被认为是相应箭图的根系统中的矢量，并证明了超适形条件将它们与虚根的某些子集相关联。这些方法还允许将Seiberg对偶解释为仿射Weyl基团在根晶格上的作用。
We generalize previous results on= 1,(3+ 1)-dimensional superconformal block quiver gauge theories. It is known that the necessary conditions for a theory to be superconformal, ie that the beta and gamma functions vanish in addition to anomaly cancellation, translate to a Diophantine equation in terms of the quiver data. We re-derive results for low block numbers revealing an new intriguing algebraic structure underlying a class of possible superconformal fixed points of such theories. After explicitly computing the five block case Diophantine equation, we use this structure to reorganize the result in a form that can be applied to arbitrary block numbers. We argue that these theories can be thought of as vectors in the root system of the corresponding quiver and superconformality conditions are shown to associate them to certain subsets of imaginary roots. These methods also allow for an interpretation of Seiberg duality as the action of the affine Weyl group on the root lattice.