论文标题
4D Chern-Simons理论和综合场理论的同位分析
Homotopical analysis of 4d Chern-Simons theory and integrable field theories
论文作者
论文摘要
本文提供了$ 4 $维的Chern-Simons理论的详细研究。使用同型理论中的技术，研究了Costello和Yamazaki提出的适当正规化版本的有限规范变换的行为。它的规格不变性与位于$ω$的极点缺陷的边界条件有关，这些缺陷由特定缺陷lie代数的各向同性谎言subergebras确定。事实证明，满足这种边界条件的磁场的类固醇等效于通过同型回调实现边界条件的群体素，从而导致边缘模式的出现。后一种观点用于阐明$ 4 $维的Chern-Simons理论产生的整合场理论。
This paper provides a detailed study of $4$-dimensional Chern-Simons theory on $\mathbb{R}^2 \times \mathbb{C}P^1$ for an arbitrary meromorphic $1$-form $ω$ on $\mathbb{C}P^1$. Using techniques from homotopy theory, the behaviour under finite gauge transformations of a suitably regularised version of the action proposed by Costello and Yamazaki is investigated. Its gauge invariance is related to boundary conditions on the surface defects located at the poles of $ω$ that are determined by isotropic Lie subalgebras of a certain defect Lie algebra. The groupoid of fields satisfying such a boundary condition is proved to be equivalent to a groupoid that implements the boundary condition through a homotopy pullback, leading to the appearance of edge modes. The latter perspective is used to clarify how integrable field theories arise from $4$-dimensional Chern-Simons theory.
