Borot, Gaëtan and Bouchard, Vincent and Chidambaram, Nitin K. and Creutzig, Thomas (2021) Whittaker vectors for $\mathcal{W}$-algebras from topological recursion. MPIM Preprint Series 2021 (11).
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Abstract
We identify Whittaker vectors for $\mathcal{W}^{\mathsf{k}}(\mathfrak{g})$-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.
| Item Type: | MPIM Preprint |
|---|---|
| Subjects: | 4 Applied mathematics / other > 81-XX Quantum theory |
| Divisions: | Research > Preprints |
| Depositing User: | Andrea Kohlhuber |
| Date Deposited: | 23 Apr 2021 10:12 |
| Last Modified: | 18 May 2021 11:02 |
| URI: | https://archive.mpim-bonn.mpg.de/id/eprint/4539 |
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