Motivated by the realisation of Yang-Baxter equation of 2d Integrable models in the 4d gauge theory of Costello-Witten-Yamazaki (CWY), we study the embedding of integrable 2d Toda field models inside this construction. This is done by using the Lax formulation of 2d integrable systems and by thinking of the standard Lax pair $L_{\pm }$ in terms of components of CWY gauge connection propagating along particular directions in the gauge bundle. We also use results of the CWY theory to build quantum line operators for 2d Toda models and compute the one loop contribution of two intersecting lines exchanging one gluon. Other features like local symmetries and comments on extension of our method to other 2d integrable models are also discussed.

中文翻译：

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来自 Lax 对的量子线算子

受 Costello-Witten-Yamazaki (CWY) 4d 规范理论中 2d 可积模型的 Yang-Baxter 方程的实现的启发，我们研究了可积 2d Toda 场模型在该结构中的嵌入。这是通过使用 2d 可积系统的 Lax 公式并通过将标准 Lax 对 $L_{\pm }$ 考虑为沿规范丛中特定方向传播的 CWY 规范连接的分量来完成的。我们还使用 CWY 理论的结果为 2d Toda 模型构建量子线算子，并计算交换一个胶子的两条相交线的一个回路贡献。还讨论了其他特征，如局部对称性和将我们的方法扩展到其他 2d 可积模型的评论。