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Super Quantum Airy Structures

Bouchard, Vincent and Ciosmak, Paweł and Hadasz, Leszek and Osuga, Kento and Ruba, Blazej and Sułkowski, Piotr (2019) Super Quantum Airy Structures. . (Submitted)

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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.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Sułkowski, Piotr0000-0002-6176-6240
Additional Information: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 P.C. is also supported by the NCN Preludium grant no. 2016/23/N/ST1/01250 “Quantum curves and Schr¨odinger equations in matrixmodels” 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.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
European Research Council (ERC)335739
European UnionPOIR.04.04.00-00-5C55/17-00
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
National Science Centre (Poland)2016/23/N/ST1/01250
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Record Number:CaltechAUTHORS:20190910-110621857
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:98543
Deposited By: Joy Painter
Deposited On:10 Sep 2019 20:45
Last Modified:11 Feb 2020 19:10

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