Seiberg-Witten配分函数中的拓扑递归：基于AGT对应
Topological Recursion in the Seiberg-Witten partition function via AGT correspondence
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中文总结 AI 辅助
本文通过AGT对应，将二维Liouville场论中的Zamolodchikov递归关系与四维Nekrasov配分函数相联系，为Seiberg-Witten理论中的拓扑递归提供了具体实例。
中文摘要 AI 辅助
本文对$\mathcal{N}=2$ $SU(N)$规范理论的Seiberg-Witten理论和瞬子微积分进行了详尽且自洽的综述。文中讨论了利用代数几何技术（如非交换分解和局域化）更高效计算瞬子配分函数的必要性。最后，利用二维共形场论（Liouville场论）与四维$\mathcal{N}=2$超对称杨-米尔斯理论之间的显著对偶性，将鲜为人知的经典Zamolodchikov递归关系[Zamolodchikov, 1987]与Nekrasov配分函数联系起来。这提供了拓扑递归的一个实例，而该递归关系若不经由此对偶，将需要高度复杂的数学才能揭示。
英文摘要
A thorough, self-contained review of Seiberg--Witten theory and instanton calculus for $\mathcal{N}=2$ $SU(N)$ gauge theory is presented. The necessity of algebro-geometric techniques---such as non-commutative resolutions and localization---for computing the instanton partition function more efficiently is discussed. Finally, a remarkable duality between 2D CFT(Liouville field theory) and 4D $\mathcal{N}=2$ SYM is used to bridge the lesser-known classical Zamolodchikov recursive relation [Zamolodchikov, 1987] and Nekrasov's partition function. This provides an instance of Topological Recursion, which would otherwise require highly sophisticated mathematics to uncover.
