Preprint 2021-01

GAE ̈TAN BOROT, VINCENT BOUCHARD, NITIN K. CHIDAMBARAM, AND THOMAS CREUTZIG

 

WHITTAKER VECTORS FOR W-ALGEBRAS FROM TOPOLOGICAL RECURSION

 

Abstract: 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.

 

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2021-01

 

79 pp.