# Super Quantum Airy Structures

## TL;DR

This paper introduces super quantum Airy structures, extending quantum Airy structures to include supersymmetry, and demonstrates their unique free energies satisfy a supersymmetric topological recursion.

## Contribution

It presents the concept of super quantum Airy structures, proves their connection to supersymmetric topological recursion, and explores their properties and classifications.

## Key findings

- Existence of unique free energies for super quantum Airy structures
- Supersymmetric generalization of topological recursion established
- Examples include superalgebras, super Frobenius algebras, and vertex operator super algebras.

## Abstract

We introduce super quantum Airy structures, which provide a supersymmetric generalization of quantum Airy structures. We prove that to a given super quantum Airy structure one can assign a unique set of free energies, which satisfy a supersymmetric generalization of the topological recursion. We reveal and discuss various properties of these supersymmetric structures, in particular their gauge transformations, classical limit, peculiar role of fermionic variables, and graphical representation of recursion relations. Furthermore, we present various examples of super quantum Airy structures, both finite-dimensional -- which include well known superalgebras and super Frobenius algebras, and whose classification scheme we also discuss -- as well as infinite-dimensional, that arise in the realm of vertex operator super algebras.