We identify Whittaker vectors for \(\mathcal {W}^{\textsf{k}}(\mathfrak {g})\)-modules with partition functions of higher Airy structures. This implies that Gaiotto vectors, describing the fundamental class in the equivariant cohomology of a suitable compactification of the moduli space of G-bundles over \(\mathbb {P}^2\) for G a complex simple Lie group, can be computed by a non-commutative version of the Chekhov–Eynard–Orantin topological recursion. We formulate the connection to higher Airy structures for Gaiotto vectors of type A, B, C, and D, and explicitly construct the topological recursion for type A (at arbitrary level) and type B (at self-dual level). On the physics side, it means that the Nekrasov partition function for pure \(\mathcal {N} = 2\) four-dimensional supersymmetric gauge theories can be accessed by topological recursion methods.

我们用更高艾里结构的配分函数确定\(\mathcal {W}^{\textsf{k}}(\mathfrak {g})\)模块的 Whittaker 向量。这意味着 Gaiotto 向量描述了G复简单李群在\(\mathbb {P}^2\)上的G模空间的适当紧化的等变上同调中的基本类，可以通过以下方式计算契诃夫-艾纳德-奥兰坦拓扑递归的非交换版本。我们为 A、B、C 和 D 类型的 Gaiotto 向量制定了与更高 Airy 结构的连接，并显式构造了 A 类型（在任意级别）和 B 类型（在自对偶级别）的拓扑递归。在物理方面，这意味着纯\(\mathcal {N} = 2\)四维超对称规范理论的 Nekrasov 配分函数可以通过拓扑递归方法来访问。