标题： 拓扑规范理论与十六个超电荷：Floer同调的更高$A_\infty$-范畴化 显示英文标题

标题： Topological Gauge Theories with Sixteen Supercharges: Higher $A_\infty$-categorification of Floer Homologies

摘要： 这项工作是[arXiv:2410.18575]的后续，也是在[arXiv:2311.18302]中启动的计划的第三和最终部分。 我们将展示如何通过某些拓扑扭曲的5d$\mathcal{N} = 2$和8d$\mathcal{N} = 1$规范理论的3d规范Landau-Ginzburg模型解释，可以推导出新颖的Fueter类型的$A_{\infty}$-2-范畴，这些范畴 2-分层化了3d-Haydys-Witten、Haydys-Witten和全纯 Donaldson-Thomas Floer同调论，分别对应于二、四和五维流形。 通过上述扭曲规范理论的2d规范Landau-Ginzburg模型解释，这些Fueter类型的$A_{\infty}$-2-范畴可以证明等价于相应的Fukaya-Seidel类型的 $A_{\infty}$-范畴。 结合来自[arXiv:2410.18575]和[arXiv:2311.18302]的先前结果，我们将提供Bousseau [3]和Doan-Rezchikov [4]的数学猜想的纯物理证明和推广。 显示英文摘要

摘要： This work is a sequel to [arXiv:2410.18575], and a third and final installment of the program initiated in [arXiv:2311.18302]. We will show how, via a 3d gauged Landau-Ginzburg model interpretation of certain topologically-twisted 5d $\mathcal{N} = 2$ and 8d $\mathcal{N} = 1$ gauge theories, one can derive novel Fueter type $A_{\infty}$-2-categories that 2-categorify the 3d-Haydys-Witten, Haydys-Witten, and holomorphic Donaldson-Thomas Floer homology of two, four, and five-manifolds, respectively. Via a 2d gauged Landau-Ginzburg model interpretation of the aforementioned twisted gauge theories, these Fueter type $A_{\infty}$-2-categories can be shown to be equivalent to corresponding Fukaya-Seidel type $A_{\infty}$-categories. Together with previous results from [arXiv:2410.18575] and [arXiv:2311.18302], we will furnish purely physical proofs and generalizations of the mathematical conjectures by Bousseau [3] and Doan-Rezchikov [4].