Super Quantum Airy Structures
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.
Additional Information
© The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. Received 21 September 2019; Accepted 19 August 2020; Published 13 October 2020. We thank Gaëtan Borot, Nitin Chidambaram, Thomas Creutzig, and Motohico Mulase for inspiring discussions. This work was supported by the ERC Starting Grant No. 335739 "Quantum fields and knot homologies" funded by the European Research Council under the European Union's Seventh Framework Programme, and the TEAM programme of the Foundation for Polish Science co-financed by the European Union under the European Regional Development Fund (POIR.04.04.00-00-5C55/17-00). V.B. and K.O. acknowledge the support of the Natural Sciences and Engineering Research Council of Canada. The work of KO is also supported in part by the Engineering and Physical Sciences Research Council under Grant Agreement Ref. EP/S003657/1. The work of P.C. is also supported by the NCN Preludium Grant No. 2016/23/N/ST1/01250 "Quantum curves and Schrödinger equations in matrix models" funded by National Science Centre in Poland. The work of B.R. was supported by the Faculty of Physics, Astronomy and Applied Computer Science Grant MSN 2019 (N17/MNS/000040) for young scientists and PhD students.Attached Files
Published - Bouchard2020_Article_SuperQuantumAiryStructures.pdf
Submitted - 1907.08913.pdf
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Additional details
- PMCID
- PMC7584568
- Eprint ID
- 98543
- Resolver ID
- CaltechAUTHORS:20190910-110621857
- 335739
- European Research Council (ERC)
- POIR.04.04.00-00-5C55/17-00
- European Union
- Natural Sciences and Engineering Research Council of Canada (NSERC)
- EP/S003657/1
- Engineering and Physical Sciences Research Council (EPSRC)
- 2016/23/N/ST1/01250
- National Science Centre (Poland)
- N17/MNS/000040
- Jagiellonian University
- Created
-
2019-09-10Created from EPrint's datestamp field
- Updated
-
2021-11-16Created from EPrint's last_modified field
- Caltech groups
- Walter Burke Institute for Theoretical Physics
- Other Numbering System Name
- CALT-TH
- Other Numbering System Identifier
- 2019-025