Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher Airy structures, W algebras and topological recursion   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
$\mathcal{W}(\mathfrak{g})$ algebras at self-dual level, with $\mathfrak{g}=
\mathfrak{gl}_{N+1}$, $\mathfrak{so}_{2 N }$ or $\mathfrak{e}_N$. 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 $\mathcal{W}$ constraints have already appeared in the literature, but we
find many new ones. For $\mathfrak{gl}_{N+1}$ 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 $\omega_{g,n}$s and is thus well defined. For all such cases,
we show that the topological recursion is equivalent to
$\mathcal{W}(\mathfrak{gl})$ constraints realized as higher quantum Airy
structures, and obtain a Givental-like decomposition for the corresponding
partition functions.

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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat