In the approach recently proposed by K. Costello and M. Yamazaki, which is based on a four-dimensional variant of Chern-Simons theory, we derive a simple and unifying two-dimensional form for the action of many integrable $\sigma$-models which are known to admit descriptions as affine Gaudin models. This includes both the Yang-Baxter deformation and the $\lambda$-deformation of the principal chiral model. We also give an interpretation of Poisson-Lie $T$-duality in this setting and derive the action of the $\mathsf{E}$-model.

中文翻译：

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来自 4D Chern–Simons 理论的可积 $$\sigma $$σ 模型的统一 2D 动作

在 K. Costello 和 M. Yamazaki 最近提出的方法中，该方法基于 Chern-Simons 理论的四维变体，我们为许多可积 $\sigma$- 的作用推导出一个简单而统一的二维形式已知承认作为仿射 Gaudin 模型的描述的模型。这包括主要手征模型的 Yang-Baxter 变形和 $\lambda$-变形。我们还在此设置中给出了泊松-李 $T$-对偶性的解释，并推导出 $\mathsf{E}$-模型的作用。