论文标题
VAFA-WITTEN理论：不变，浮点同源物，希格斯捆绑包，几何兰兰兹通讯和分类
Vafa-Witten Theory: Invariants, Floer Homologies, Higgs Bundles, a Geometric Langlands Correspondence, and Categorification
论文作者
论文摘要
我们在更通用的环境中重新审视瓦法理论，基本的模量空间不是Instantons，而是完整的VAFA式方程式的空间。我们在物理上得出（i）与此模量空间相关的新型VAFA字体四个manifold不变性，（ii）与Gromov-Witten不变性的关系，（iii）一种新颖的VAFA-Witten Floer同源性，分配给了三个manifold界限，（iv）由小说vafa atiyah-witten atiyah-floer（iventer）vafa atiyah-floer（iventen atiyah-floeriative）（v） Abouzaid-Manolescu in [1] about the hypercohomology of a perverse sheaf of vanishing cycles, (vi) a Langlands duality of these invariants, Floer homologies and hypercohomology, and (vii) a quantum geometric Langlands correspondence with purely imaginary parameter that specializes to the classical correspondence in the zero-coupling limit, where Higgs bundles feature in （ii），（iv），（vi）和（vii）。我们还解释了这些不变性和同源性如何在此过程中分类，并讨论它们的更高分类。因此，我们通过在数学中使用的差异和枚举几何形状，拓扑和几何表示理论，通过最大含量的拓扑量子场理论与物理学中的电磁二重性有关。
We revisit Vafa-Witten theory in the more general setting whereby the underlying moduli space is not that of instantons, but of the full Vafa-Witten equations. We physically derive (i) a novel Vafa-Witten four-manifold invariant associated with this moduli space, (ii) their relation to Gromov-Witten invariants, (iii) a novel Vafa-Witten Floer homology assigned to three-manifold boundaries, (iv) a novel Vafa-Witten Atiyah-Floer correspondence, (v) a proof and generalization of a conjecture by Abouzaid-Manolescu in [1] about the hypercohomology of a perverse sheaf of vanishing cycles, (vi) a Langlands duality of these invariants, Floer homologies and hypercohomology, and (vii) a quantum geometric Langlands correspondence with purely imaginary parameter that specializes to the classical correspondence in the zero-coupling limit, where Higgs bundles feature in (ii), (iv), (vi) and (vii). We also explain how these invariants and homologies will be categorified in the process, and discuss their higher categorification. We therefore relate differential and enumerative geometry, topology and geometric representation theory in mathematics, via a maximally-supersymmetric topological quantum field theory with electric-magnetic duality in physics.
