Bouchard Vincent, Ciosmak Paweł, Hadasz Leszek, Osuga Kento, Ruba Błażej, Sułkowski Piotr
Department of Mathematical and Statistical Sciences, University of Alberta, 632 CAB, Edmonton, AB T6G 2G1 Canada.
Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland.
Commun Math Phys. 2020;380(1):449-522. doi: 10.1007/s00220-020-03876-0. Epub 2020 Oct 13.
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.
我们引入了超量子艾里结构，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，可以赋予其一组唯一的自由能，这些自由能满足拓扑递归的超对称推广。我们揭示并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，我们给出了超量子艾里结构的各种例子，包括有限维的——其中包括著名的超代数和超弗罗贝尼乌斯代数，我们还讨论了它们的分类方案——以及无限维的，这些例子出现在顶点算子超代数领域。
