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.

arXiv comment38 pages, presentation changed, accepted version in LMP

References in corpus (29)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Supersymmetric vacua and Bethe ansatz
• Quantum integrability and supersymmetric vacua
• Instanton counting on blowup. I. 4-dimensional pure gauge theory
• Free energy topological expansion for the 2-matrix model
• BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters
• Asymptotically free N=2 theories and irregular conformal blocks
• Multi instanton calculus on ALE spaces
• Super Liouville conformal blocks from N=2 SU(2) quiver gauge theories
• Gauge Theories on ALE Space and Super Liouville Correlation Functions
• BPS/CFT Correspondence III: Gauge Origami partition function and qq-characters
• Algebraic methods in random matrices and enumerative geometry
• BPS/CFT correspondence IV: sigma models and defects in gauge theory
• Instantons and 2d Superconformal field theory
• Think globally, compute locally
• Ramond sector of super Liouville theory from instantons on an ALE space
• A slow review of the AGT correspondence
• The ABCD of topological recursion
• Instanton moduli spaces and $\mathcal{W}$-algebras
• A brief review of the 2d/4d correspondences
• BPS/CFT correspondence V: BPZ and KZ equations from qq-characters
• Lectures on Instanton Counting
• Super Quantum Airy Structures
• From CFT to Ramond super-quantum curves
• Supereigenvalue Models and Topological Recursion
• Topological Recursion in The Ramond Sector
• Whittaker vectors for $\mathcal{W}$-algebras from topological recursion
• $n$-th parafermion ${\mathcal{W}}_N$ characters from $U(N)$ instanton counting on ${\mathbb{C}}^2/{\mathbb{Z}}_n$
• $\mathcal{N}=1$ Super Topological Recursion

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