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.

中文翻译：

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超量子艾里结构

我们介绍了超量子艾里结构，它提供了量子艾里结构的超对称推广。我们证明，对于给定的超量子艾里结构，可以分配一组独特的自由能，满足拓扑递归的超对称推广。我们揭示和讨论了这些超对称结构的各种性质，特别是它们的规范变换、经典极限、费米子变量的特殊作用以及递归关系的图形表示。此外，我们提出了各种超量子艾里结构的例子，包括有限维的——包括众所周知的超代数和超 Frobenius 代数，我们也讨论了它们的分类方案——以及在顶点算子领域出现的无限维。超级代数。