• Corpus ID: 222177514

# Higher Airy structures and topological recursion for singular spectral curves

@article{Borot2020HigherAS,
title={Higher Airy structures and topological recursion for singular spectral curves},
author={Gaetan Borot and Reinier Kramer and Yannik Schuler},
journal={arXiv: Mathematical Physics},
year={2020}
}
• Published 7 October 2020
• Mathematics
• arXiv: Mathematical Physics
We give elements towards the classification of quantum Airy structures based on the $W(\mathfrak{gl}_r)$-algebras at self-dual level based on twisted modules of the Heisenberg VOA of $\mathfrak{gl}_r$ for twists by arbitrary elements of the Weyl group $\mathfrak{S}_{r}$. In particular, we construct a large class of such quantum Airy structures. We show that the system of linear ODEs forming the quantum Airy structure and determining uniquely its partition function is equivalent to a topological…

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## References

SHOWING 1-10 OF 66 REFERENCES

• Mathematics
• 2021
We produce in an explicit form free generators of the afﬁne W -algebra of type A associated with a nilpotent matrix whose Jordan blocks are of the same size. This includes the principal nilpotent
• Mathematics
• 2021
We lay the foundation for a version of $r$-spin theory in genus zero for Riemann surfaces with boundary. In particular, we define the notion of $r$-spin disks, their moduli space, and the Witten
• Mathematics
• 2020
We lay the foundation for a version of $r$-spin theory in genus zero for Riemann surfaces with boundary. In particular, we define the notion of $r$-spin disks, their moduli space, and the Witten
The first topic of this dissertation is the moduli space of curves. I define half-spin relations, specialising Pandharipande-Pixton-Zvonkine’s spin relations, to reprove Buryak-Shadrin-Zvonkine’s
• Physics
• 2009
One of the fundamental problems of the theory of second-order phase transitions is the description of all possible types of universal critical behavior. If one adopts the hypothesis of conformal
• Mathematics
• 2019
We prove the 2006 Zvonkine conjecture that expresses Hurwitz numbers with completed cycles in terms of intersection numbers with the Chiodo classes via the so-called $r$-ELSV formula, as well as its
• Mathematics
• 2016
We derive a Bouchard–Eynard type topological recursion for the total descendant potential of AN-singularity. Our argument relies on a certain twisted representation of a Heisenberg Vertex Operator
We show that two natural approaches to quantum gravity coincide. This identity is nontrivial and relies on the equivalence of each approach to KdV equations. We also investigate related mathematical