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，并且是始于[arXiv:2311.18302]的项目的第三部分和最终部分。 我们展示了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2-范畴对3d-Haydys-Witten、Haydys-Witten以及分别对应于两、四和五流形的全纯Donaldson-Thomas Floer同调进行了2-范畴化。 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-范畴可以被证明等价于相应的Fukaya-Seidel类型的$A_{\infty}$-范畴。 在8d情况下，还可以推导出更高阶的$A_{\infty}$-范畴，例如一种新颖的Cauchy-Riemann-Fueter类型的$A_{\infty}$-3-范畴，该范畴通过理论的4d规范Landau-Ginzburg模型解释对四流形的Haydys-Witten Floer同调进行了3-范畴化。 结合来自[arXiv:2410.18575]和[arXiv:2311.18302]的先前结果，我们的工作提供了Bousseau [3]、Doan-Rezchikov [4]和Cao [5]提出的数学猜想的纯粹物理证明和推广。 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 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. In the 8d case, one can also derive higher $A_{\infty}$-categories, such as a novel Cauchy-Riemann-Fueter type $A_{\infty}$-3-category that 3-categorifies the Haydys-Witten Floer homology of four-manifolds via a 4d gauged Landau-Ginzburg model interpretation of the theory. Together with previous results from [arXiv:2410.18575] and [arXiv:2311.18302], our work furnishes purely physical proofs and generalizations of the mathematical conjectures by Bousseau [3], Doan-Rezchikov [4], and Cao [5].