Whittaker vectors for W-algebras from topological recursion

Borot G, Bouchard V, Chidambaram NK, Creutzig T (2024)

Publication Type: Journal article

Publication year: 2024

Journal

Selecta Mathematica-New Series Springer Verlag (Germany)

Book Volume: 30

Article Number: 33

Journal Issue: 2

DOI: 10.1007/s00029-024-00921-x

Abstract

We identify Whittaker vectors for W^k(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 P² 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 N=2 four-dimensional supersymmetric gauge theories can be accessed by topological recursion methods.

Authors with CRIS profile

Thomas Creutzig

Involved external institutions

Humboldt-Universität zu Berlin

Germany (DE) University of Alberta

Canada (CA) Max-Planck-Institut für Mathematik (MPIM)

Germany (DE)

How to cite

APA:

Borot, G., Bouchard, V., Chidambaram, N.K., & Creutzig, T. (2024). Whittaker vectors for W-algebras from topological recursion. Selecta Mathematica-New Series, 30(2). https://doi.org/10.1007/s00029-024-00921-x

MLA:

Borot, Gaëtan, et al. "Whittaker vectors for W-algebras from topological recursion." Selecta Mathematica-New Series 30.2 (2024).

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