Whittaker vectors forW-algebras from topological recursion

• Gaëtan Borot ^[2] ; Vincent Bouchard ^[3] ; Nitin K. Chidambaram ^[1] ; Thomas Creutzig ^[3]
  1. [1] University of Edinburgh

     University of Edinburgh

     Reino Unido

     
  2. [2] Institut für Mathematik und Institut für Physik, Humboldt-Universität zu Berlin,Germany
  3. [3] Department of Mathematical and Statistical Sciences, University of Alberta,Canada

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 2, 2024, 91 págs.
• Idioma: inglés
• DOI: 10.1007/s00029-024-00921-x
• Enlaces
  • Texto completo
• Resumen

  • We identify Whittaker vectors for Wk(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.

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