标题： 来自.twistor空间的可积变形 显示英文标题

标题： Integrable Deformations from Twistor Space

摘要： 二维可积场论被知源于四维Chern-Simons理论的缺陷理论以及四维反自对偶Yang-Mills方程的对称约化。基于Costello的想法，在Bittleston和Skinner的工作中提出，这两种方法可以通过从六维全纯Chern-Simons理论开始统一起来。我们首次完整描述了这一系列可积理论的“钻石结构”，适用于一类变形sigma模型，超越了迄今为止所考虑的Dirichlet边界条件。从扭量空间上的六维全纯Chern-Simons理论出发，该理论具有特定的亚纯三形式$\Omega$，我们构造出缺陷理论，从而得到一种新的四维可积场论，其运动方程可以重新表述为四维反自对偶Yang-Mills方程。通过对称约化，我们得到了一个多参数的二维可积模型，在参数空间的某个点上特化为$\lambda$-变形。同样的模型也可以通过先对称约化（给出具有一般边界条件的四维Chern-Simons理论），然后构造缺陷理论来恢复。 显示英文摘要

摘要： Integrable field theories in two dimensions are known to originate as defect theories of 4d Chern-Simons and as symmetry reductions of the 4d anti-self-dual Yang-Mills equations. Based on ideas of Costello, it has been proposed in work of Bittleston and Skinner that these two approaches can be unified starting from holomorphic Chern-Simons in 6 dimensions. We provide the first complete description of this diamond of integrable theories for a family of deformed sigma models, going beyond the Dirichlet boundary conditions that have been considered thus far. Starting from 6d holomorphic Chern-Simons theory on twistor space with a particular meromorphic 3-form $\Omega$, we construct the defect theory to find a novel 4d integrable field theory, whose equations of motion can be recast as the 4d anti-self-dual Yang-Mills equations. Symmetry reducing, we find a multi-parameter 2d integrable model, which specialises to the $\lambda$-deformation at a certain point in parameter space. The same model is recovered by first symmetry reducing, to give 4d Chern-Simons with generalised boundary conditions, and then constructing the defect theory.