We investigate a relation between the super topological recursion and Gaiotto
vectors for N=1 superconformal blocks. Concretely, we introduce the
notion of the untwisted and μ-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 N=1 superconformal blocks in
the Neveu-Schwarz or Ramond sector. Equivalently, the Gaiotto vector can be
computed by the untwisted or μ-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 N=2 pure U(2) supersymmetric gauge theory on
C2/Z2​ via a conjectural extension of the
Alday-Gaiotto-Tachikawa correspondence.Comment: 37 pages, references added, typos correcte