• Corpus ID: 233204298

Whittaker vectors for $\mathcal{W}$-algebras from topological recursion

@inproceedings{Borot2021WhittakerVF,
  title={Whittaker vectors for \$\mathcal\{W\}\$-algebras from topological recursion},
  author={Gaetan Borot and Vincent Bouchard and Nitin Kumar Chidambaram and Thomas Creutzig},
  year={2021}
}

• G. Borot, V. Bouchard, +1 author T. Creutzig
• Published 9 April 2021
• Mathematics

We identify Whittaker vectors for $\mathcal{W}_k(\mathfrak{g})$-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.