标题： 可积变形来自扭形空间 显示英文标题

标题： Integrable Deformations from Twistor Space

摘要： 二维可积场论已知起源于四维Chern-Simons的缺陷理论，并作为四维自对偶Yang-Mills方程的对称性约化。 基于Costello的想法，Bittleston和Skinner的工作中提出，这两种方法可以从六维全纯Chern-Simons理论出发进行统一。 我们为一类变形sigma模型提供这种可积理论菱形的首次完整描述，超越了迄今为止所考虑的狄利克雷边界条件。 从扭量空间上的六维全纯Chern-Simons理论开始，使用特定的有理3形式$\Omega$，我们构造缺陷理论，发现一种新颖的四维可积场论，其运动方程可以重新表述为四维自对偶Yang-Mills方程。 通过对称性约化，我们找到一个多参数的二维可积模型，在参数空间的某一点上，它特化为$\lambda$变形。 同样的模型也可以通过先对称性约化得到具有广义边界条件的四维Chern-Simons，然后再构造缺陷理论来获得。 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.