标题： 二维格点杨-米尔斯理论的导出代数几何 显示英文标题

标题： Derived algebraic geometry of 2d lattice Yang-Mills theory

摘要： 对经典$\mathrm{GL}_n$-Yang-Mills 理论在$2$维平方格点$\mathbb{Z}^2$上的导出代数几何研究被提出。 威尔逊作用的导出临界点被描述，并提取了在矩形子集$V =[a,b]\times [c,d]\subseteq \mathbb{Z}^2$上局部数据，其两边长度为$\geq 2$。 从局部数据的导出栈上的完美复形的 dg-范畴构造了一个在$\mathbb{Z}^2$上的局部常数 dg-范畴值的预因子代数。 显示英文摘要

摘要： A derived algebraic geometric study of classical $\mathrm{GL}_n$-Yang-Mills theory on the $2$-dimensional square lattice $\mathbb{Z}^2$ is presented. The derived critical locus of the Wilson action is described and its local data supported in rectangular subsets $V =[a,b]\times [c,d]\subseteq \mathbb{Z}^2$ with both sides of length $\geq 2$ is extracted. A locally constant dg-category-valued prefactorization algebra on $\mathbb{Z}^2$ is constructed from the dg-categories of perfect complexes on the derived stacks of local data.