2024/12/28 by Arif Er, Er, Arif, Meng-Chwan Tan +1
Computer Science · Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2412.20067
openalex publication_date 2024/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 N = 2 and 8d N = 1 gauge theories, one can derive novel Fueter type A∞-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∞-2-categories can be shown to be equivalent to corresponding Fukaya-Seidel type A∞-categories. In the 8d case, one can also derive higher A∞-categories, such as a novel Cauchy-Riemann-Fueter type A∞-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].