Super Topological Recursion and Gaiotto Vectors For Superconformal Blocks

Abstract

We investigate a relation between the super topological recursion and Gaiotto vectors for $\mathcal{N}=1$ superconformal blocks. Concretely, we introduce the notion of the untwisted and $\mu$-twisted super topological recursion, and construct a dual algebraic description in terms of super Airy structures. We then show that the partition function of an appropriate super Airy structure coincides with the Gaiotto vector for $\mathcal{N}=1$ superconformal blocks in the Neveu-Schwarz or Ramond sector. Equivalently, the Gaiotto vector can be computed by the untwisted or $\mu$-twisted super topological recursion. This implies that the framework of the super topological recursion -- equivalently super Airy structures -- can be applied to compute the Nekrasov partition function of $\mathcal{N}=2$ pure $U(2)$ supersymmetric gauge theory on ${\mathbb{C}}^2/{\mathbb{Z}}_2$ via a conjectural extension of the Alday-Gaiotto-Tachikawa correspondence.

38 pages, presentation changed, accepted version in LMP

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Cited by in corpus (4)

• Whittaker vectors for $\mathcal{W}$-algebras from topological recursion
• Quantum curves from refined topological recursion: the genus 0 case
• Taking limits in topological recursion
• Refined topological recursion revisited -- properties and conjectures