Super Topological Recursion and Gaiotto Vectors For Superconformal Blocks

• Main Author: Osuga, Kento
• Format: Journal Article
• Language: English
• Published: 17-05-2022
• Subjects: Mathematics - Mathematical Physics; Physics - High Energy Physics - Theory; Physics - Mathematical Physics
• DOI: 10.48550/arxiv.2107.04588

Lett Math Phys 112, 48 (2022) 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.