تقرير
Topological 5d $\mathcal {N} = 2$ Gauge Theory: Novel Floer Homologies, their Dualities, and an $A_\infty$-category of Three-Manifolds
| العنوان: | Topological 5d $\mathcal {N} = 2$ Gauge Theory: Novel Floer Homologies, their Dualities, and an $A_\infty$-category of Three-Manifolds |
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| المؤلفون: | Er, Arif, Ong, Zhi-Cong, Tan, Meng-Chwan |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics High Energy Physics - Theory |
| مصطلحات موضوعية: | High Energy Physics - Theory, Mathematics - Algebraic Geometry, Mathematics - Differential Geometry, Mathematics - Geometric Topology, Mathematics - Symplectic Geometry |
| الوصف: | We show how one can define novel gauge-theoretic Floer homologies of four, three and two-manifolds from the physics of a certain topologically-twisted 5d ${\cal N}=2$ gauge theory via its supersymmetric quantum mechanics interpretation. They are associated with Vafa-Witten, Hitchin and $G_{\mathbb{C}}$-BF configurations on the four, three and two-manifolds, respectively. We also show how one can define novel symplectic Floer homologies of Hitchin spaces, which in turn will allow us to derive novel Atiyah-Floer correspondences that relate our gauge-theoretic Floer homologies to symplectic intersection Floer homologies of Higgs bundles. Furthermore, topological invariance and 5d "S-duality" suggest a web of relations and a Langlands duality amongst these novel Floer homologies and their loop/toroidal group generalizations. Last but not least, via a 2d gauged Landau-Ginzburg model interpretation of the 5d theory, we derive, from the soliton string theory that it defines and the 5d partition function, a Fukaya-Seidel type $A_\infty$-category of Hitchin configurations on three-manifolds and its novel Atiyah-Floer correspondence. Our work therefore furnishes purely physical proofs and generalizations of the mathematical conjectures of Haydys [1], Abouzaid-Manolescu [2], and Bousseau [3], and more. Comment: 61 pp. Additional material in Section 9 which physically proves and generalizes Bousseau's mathematical conjecture in [3] |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2311.18302 |
| رقم الأكسشن: | edsarx.2311.18302 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |