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Singular vector structure of quantum curves

Ciosmak, Paweł and Hadasz, Leszek and Manabe, Masahide and Sułkowski, Piotr (2018) Singular vector structure of quantum curves. In: Topological Recursion and its Influence in Analysis, Geometry, and Topology. Proceedings of Symposia in Pure Mathematics. No.100. American Mathematical Society , Providence, RI, pp. 119-149. ISBN 978-1-4704-3541-7. http://resolver.caltech.edu/CaltechAUTHORS:20190206-115727828

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Abstract

We show that quantum curves arise in infinite families and have the structure of singular vectors of a relevant symmetry algebra. We analyze in detail the case of the hermitian one-matrix model with the underlying Virasoro algebra, and the super-eigenvalue model with the underlying super-Virasoro algebra. In the Virasoro case we relate singular vector structure of quantum curves to the topological recursion, and in the super-Virasoro case we introduce the notion of super-quantum curves. We also discuss the double quantum structure of the quantum curves and analyze specific examples of Gaussian and multi-Penner models.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1090/pspum/100/01766 DOIArticle
https://bookstore.ams.org/pspum-100PublisherBook Publisher
https://arxiv.org/abs/1711.08031arXivDiscussion Paper
Additional Information:© 2018 American Mathematical Society. We are grateful to the American Mathematical Society for the organization of the 2016 AMS von Neumann Symposium “Topological Recursion and its Influence in Analysis, Geometry, and Topology”. P.S. is indebted to Bertrand Eynard, Chiu-Chu Melissa Liu, and Motohico Mulase for providing the opportunity to present these results, inspiration and encouragement. We also thank Vincent Bouchard, Zbigniew Jaskólski and Chaiho Rim for discussions. This work is 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.
Group:Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
European Research Council (ERC)335739
Record Number:CaltechAUTHORS:20190206-115727828
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20190206-115727828
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92740
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:06 Feb 2019 20:16
Last Modified:06 Feb 2019 20:16

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