Topological 5d $\mathcal{N} = 2$ Gauge Theories: Mirror Symmetry and Langlands Duality of $A_\infty$-categories of Floer Homologies
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918410192945152 |
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| author | Er, Arif Tan, Meng-Chwan |
| author_facet | Er, Arif Tan, Meng-Chwan |
| contents | We explain why on certain five-manifolds, topological 5d $\mathcal{N} = 2$ gauge theory of Haydys-Witten twist with gauge group $G$, is dual to that of Geyer-Mülsch twist with gauge group $^LG$, where $G$ is a real, compact Lie group with Langlands dual $^LG$. In turn, via their 2d and 3d gauged A/B-twisted Landau-Ginzburg model interpretations, we can show that (i) a Fukaya-Seidel-type $A_\infty$-1-category of an HW$_4$-instanton Floer homology of three-manifolds and (ii) a Fueter-type $A_\infty$-2-category of an HW$_3$-instanton Floer homology of two-manifolds, are dual to (i) an Orlov-type $A_\infty$-1-category of a novel holomorphic $^LG_{\mathbb{H}}$-flat Floer homology of three-manifolds and (ii) a Rozansky-Witten-type $A_\infty$-2-category of a novel holomorphic $^LG_{\mathbb{O}}$-flat Floer homology of two-manifolds, respectively. We also derive their Atiyah-Floer-type correspondences to symplectic categories. Our work, which demonstrates a mirror symmetry and Langlands duality of (higher) $A_\infty$-categories of Floer homologies, therefore furnishes purely physical proofs and gauge-theoretic generalizations of the mathematical conjectures by Bousseau [1] and Doan-Rezchikov [2], and more. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_15953 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topological 5d $\mathcal{N} = 2$ Gauge Theories: Mirror Symmetry and Langlands Duality of $A_\infty$-categories of Floer Homologies Er, Arif Tan, Meng-Chwan High Energy Physics - Theory Algebraic Geometry Differential Geometry Geometric Topology Symplectic Geometry We explain why on certain five-manifolds, topological 5d $\mathcal{N} = 2$ gauge theory of Haydys-Witten twist with gauge group $G$, is dual to that of Geyer-Mülsch twist with gauge group $^LG$, where $G$ is a real, compact Lie group with Langlands dual $^LG$. In turn, via their 2d and 3d gauged A/B-twisted Landau-Ginzburg model interpretations, we can show that (i) a Fukaya-Seidel-type $A_\infty$-1-category of an HW$_4$-instanton Floer homology of three-manifolds and (ii) a Fueter-type $A_\infty$-2-category of an HW$_3$-instanton Floer homology of two-manifolds, are dual to (i) an Orlov-type $A_\infty$-1-category of a novel holomorphic $^LG_{\mathbb{H}}$-flat Floer homology of three-manifolds and (ii) a Rozansky-Witten-type $A_\infty$-2-category of a novel holomorphic $^LG_{\mathbb{O}}$-flat Floer homology of two-manifolds, respectively. We also derive their Atiyah-Floer-type correspondences to symplectic categories. Our work, which demonstrates a mirror symmetry and Langlands duality of (higher) $A_\infty$-categories of Floer homologies, therefore furnishes purely physical proofs and gauge-theoretic generalizations of the mathematical conjectures by Bousseau [1] and Doan-Rezchikov [2], and more. |
| title | Topological 5d $\mathcal{N} = 2$ Gauge Theories: Mirror Symmetry and Langlands Duality of $A_\infty$-categories of Floer Homologies |
| topic | High Energy Physics - Theory Algebraic Geometry Differential Geometry Geometric Topology Symplectic Geometry |
| url | https://arxiv.org/abs/2511.15953 |