论文标题
扭曲器，ASD Yang-Mills方程和4D Chern-Simons理论
Twistors, the ASD Yang-Mills equations, and 4d Chern-Simons theory
论文作者
论文摘要
我们表明，通过4D Chern-Simons理论以及通过反对偶义扬米尔斯方程的对称性降低对整合系统的方法至少是密切相关的，至少是经典的。按照凯文·科斯特洛（Kevin Costello）的建议，我们从关于扭曲空间的全体形态切尔 - 西蒙斯（Chern-Simons）理论开始，该理论在借助于meromorphic（3,0）-form $ω$的帮助下定义。如果$ω$无处可消失，它将降至4D时空的理论，其经典运动方程等于反对双重扬·米尔斯方程。示例包括WESS-Zumino-witten模型的4D类似物，以及具有立方两个导数相互作用的Lie代数标量的理论。在减少对称性的情况下，这些屈服动作对2D可集成系统。另一方面，直接在扭曲器空间上进行对称性降低，将全体形态的Chern-Simons理论降低到4D Chern-Simons理论，并具有由Costello＆Yamazaki研究的混乱缺陷。最后，我们表明，单个翻译的类似降低导致了描述Bogomolny方程的5D部分全体形态的Chern-Simons理论。
We show that the approaches to integrable systems via 4d Chern-Simons theory and via symmetry reductions of the anti-self-dual Yang-Mills equations are closely related, at least classically. Following a suggestion of Kevin Costello, we start from holomorphic Chern-Simons theory on twistor space, defined with the help of a meromorphic (3,0)-form $Ω$. If $Ω$ is nowhere vanishing, it descends to a theory on 4d space-time with classical equations of motion equivalent to the anti-self-dual Yang-Mills equations. Examples include a 4d analogue of the Wess-Zumino-Witten model and a theory of a Lie algebra valued scalar with a cubic two derivative interaction. Under symmetry reduction, these yield actions for 2d integrable systems. On the other hand, performing the symmetry reduction directly on twistor space reduces holomorphic Chern-Simons theory to the 4d Chern-Simons theory with disorder defects studied by Costello & Yamazaki. Finally we show that a similar reduction by a single translation leads to a 5d partially holomorphic Chern-Simons theory describing the Bogomolny equations.
