Whittaker vectors for W-algebras from topological recursion

Abstract: Gaiotto vectors, describing the fundamental class in the equivariant cohomology of a suitable compactification of the moduli space of G-bundles over P^2, for G a complex simple Lie group, are Whittaker vectors for modules of W-algebras. In this work we identify these Whittaker vectors with partition functions of quantum Airy structures, which means that they can be calculated by topological recursion methods. On the physics side, it means that the Nekrasov partition function for pure N=2 4d supersymmetric gauge theories can be accessed via a topological recursion à la Chekhov-Eynard-Orantin. We formulate the connection for Gaiotto vectors of type A, B, C, and D. For those interested in topological recursion, the type A case at arbitrary level gives rise to a new non-commutative formulation of topological recursion.

HEP - theorymathematical physicsalgebraic geometrycombinatoricsexactly solvable and integrable systems

Audience: researchers in the discipline

IBS-CGP Mathematical Physics Seminar

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