We elucidate how integrable lattice models described by Costello's 4d Chern-Simons theory can be realized via a stack of D4-branes ending on an NS5-brane in type IIA string theory, with D0-branes on the D4-brane worldvolume sourcing a meromorphic RR 1-form, and fundamental strings forming the lattice. This provides us with a nonperturbative integration cycle for the 4d Chern-Simons theory, and by applying T- and S-duality, we show how the R-matrix, the Yang-Baxter equation and the Yangian can be categorified, that is, obtained via the Hilbert space of a 6d gauge theory.

中文翻译：

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膜和分类可积点阵模型

我们阐明了 Costello 的 4d Chern-Simons 理论描述的可积晶格模型如何通过 IIA 型弦理论中以 NS5-膜结尾的一堆 D4-膜来实现，D4-膜世界体积上的 D0-膜采购亚纯 RR 1-形式，以及形成格子的基本弦。这为我们提供了 4d Chern-Simons 理论的非微扰积分循环，并且通过应用 T-和 S-对偶，我们展示了如何对 R-矩阵、Yang-Baxter 方程和 Yangian 进行分类，即获得通过 6d 规范理论的希尔伯特空间。