We establish a correspondence between a class of Wilson-’t Hooft lines in four-dimensional N $$ \mathcal{N} $$ = 2 supersymmetric gauge theories described by circular quivers and transfer matrices constructed from dynamical L-operators for trigonometric quantum integrable systems. We compute the vacuum expectation values of the Wilson-’t Hooft lines in a twisted product space S 1 × ϵ ℝ 2 × ℝ by supersymmetric localization and show that they are equal to the Wigner transforms of the transfer matrices. A variant of the AGT correspondence implies an identification of the transfer matrices with Verlinde operators in Toda theory, which we also verify. We explain how these field theory setups are related to four-dimensional Chern-Simons theory via embedding into string theory and dualities.

中文翻译：

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Wilson-'t Hooft 线作为传递矩阵

我们在四维 N $$ \mathcal{N} $$ = 2 超对称规范理论中建立了一类 Wilson-'t Hooft 线之间的对应关系，这些规范由圆形颤动描述，以及由三角量子可积的动态 L 算子构造的传递矩阵系统。我们通过超对称定位计算了扭曲积空间 S 1 × ϵ ℝ 2 × ℝ 中 Wilson-'t Hooft 线的真空期望值，并表明它们等于传递矩阵的 Wigner 变换。AGT 对应的一个变体意味着使用 Toda 理论中的 Verlinde 算子识别转移矩阵，我们也验证了这一点。我们通过嵌入弦论和对偶来解释这些场论设置如何与四维陈-西蒙斯理论相关。