We describe a general method to determine dualities between supersymmetric 5d gauge theories. The method is based on performing local S-dualities in the geometry associated to the gauge theory. We find that often a duality can be obtained by adding matter to both sides of a more primitive duality. This allows us to define the notion of irreducible dualities which cannot be obtained from more primitive dualities. More general dualities then are obtained by adding matter to both sides of an irreducible duality. The geometric method described in this paper allows us to systematically construct irreducible dualities. As an application, we explicitly determine a special class of irreducible dualities classified by removal and addition of edges into a Dynkin diagram. This class of dualities vastly generalizes many of the known 5d dualities in the literature.

中文翻译：

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来自 S-对偶的 5d 规范理论的对偶性

我们描述了一种确定超对称 5d 规范理论之间对偶性的一般方法。该方法基于在与规范理论相关的几何中执行局部 S 对偶。我们发现通常可以通过在更原始的二元性的两侧添加物质来获得二元性。这使我们能够定义无法从更原始的二元性中获得的不可约二元性的概念。然后通过在不可约的二元性的两侧添加物质来获得更一般的二元性。本文中描述的几何方法使我们能够系统地构建不可约的二元性。作为一个应用，我们明确地确定了一类特殊的不可约对偶，通过去除和添加边到 Dynkin 图来分类。