Higher Airy Structures, đť’˛ Algebras and Topological Recursion Article Swipe
Gaëtan Borot
,
Vincent Bouchard
,
Nitin Kumar Chidambaram
,
Thomas Creutzig
,
Dmitry Noshchenko
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1090/memo/1476
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1090/memo/1476
We define higher quantum Airy structures as generalizations of the Kontsevich–Soibelman quantum Airy structures by allowing differential operators of arbitrary order (instead of only quadratic). We construct many classes of examples of higher quantum Airy structures as modules of algebras at self-dual level, with , or . We discuss their enumerative geometric meaning in the context of (open and closed) intersection theory of the moduli space of curves and its variants. Some of these constraints have already appeared in the literature, but we find many new ones. For our result hinges on the description of previously unnoticed Lie subalgebras of the algebra of modes. As a consequence, we obtain a simple characterization of the spectral curves (with arbitrary ramification) for which the Bouchard–Eynard topological recursion gives symmetric s and is thus well defined. For all such cases, we show that the topological recursion is equivalent to constraints realized as higher quantum Airy structures, and obtain a Givental-like decomposition for the corresponding partition functions.
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- article
- Language
- en
- Landing Page
- https://doi.org/10.1090/memo/1476
- https://www.ams.org/memo/1476/memo1476.pdf
- OA Status
- bronze
- Cited By
- 12
- References
- 87
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4393950498
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Higher Airy Structures, đť’˛ Algebras and Topological RecursionWork title
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articleOpenAlex work type
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enPrimary language
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2024Year of publication
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2024-04-01Full publication date if available
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Gaëtan Borot, Vincent Bouchard, Nitin Kumar Chidambaram, Thomas Creutzig, Dmitry NoshchenkoList of authors in order
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https://doi.org/10.1090/memo/1476Publisher landing page
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https://www.ams.org/memo/1476/memo1476.pdfDirect link to full text PDF
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Recursion (computer science), Mathematics, Pure mathematics, Algebra over a field, Topology (electrical circuits), Combinatorics, AlgorithmTop concepts (fields/topics) attached by OpenAlex
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