论文标题
可集成的$ \ MATHCAL {E} $ - 模型，4D Chern-Simons理论和Aggine Gaudin模型。 I.拉格朗日方面
Integrable $\mathcal{E}$-Models, 4d Chern-Simons Theory and Affine Gaudin Models. I. Lagrangian Aspects
论文作者
论文摘要
我们构建了一个非常广阔的2D $σ$模型家族的动作。我们的起点是使用Costello和Yamazaki的框架在[Arxiv：2008.01829]中获得的通用2D动作，基于4D Chern-Simons理论。这2D操作取决于一对2D字段$ h $和$ \ nathcal {l} $，并取决于$ \ nathcal {l} $，取决于辅助复杂参数，这些参数是由约束捆绑在一起的。当后者可以用$ \ Mathcal {l} $以$ h $求解时，这将为2D字段$ h $产生2D集成字段理论，其LAX连接由$ \ Mathcal {l}（H）$提供。我们构建了该约束的一般解决方案类别，并表明所得的2D集成字段理论自然都可以描述为$ \ Mathcal {e} $ - 模型。
We construct the actions of a very broad family of 2d integrable $σ$-models. Our starting point is a universal 2d action obtained in [arXiv:2008.01829] using the framework of Costello and Yamazaki based on 4d Chern-Simons theory. This 2d action depends on a pair of 2d fields $h$ and $\mathcal{L}$, with $\mathcal{L}$ depending rationally on an auxiliary complex parameter, which are tied together by a constraint. When the latter can be solved for $\mathcal{L}$ in terms of $h$ this produces a 2d integrable field theory for the 2d field $h$ whose Lax connection is given by $\mathcal{L}(h)$. We construct a general class of solutions to this constraint and show that the resulting 2d integrable field theories can all naturally be described as $\mathcal{E}$-models.
