Ramifications of Hurwitz theory, KP integrability and quantum curves
A. Alexandrov, D. Lewanski, and S. Shadrin
TL;DR
This paper explores the connections between Hurwitz numbers, KP integrability, and quantum curves, providing new proofs and examples of quantum spectral curves for double Hurwitz numbers.
Contribution
It introduces new methods for deriving quantum spectral curves from Hurwitz numbers within the KP integrability framework and presents novel examples for double Hurwitz numbers.
Findings
New proofs for monotone Hurwitz numbers
Derivation of quantum curves for double Hurwitz numbers
Enhanced understanding of the relationship between Hurwitz theory and quantum curves
Abstract
In this paper we revisit several recent results on monotone and strictly monotone Hurwitz numbers, providing new proofs. In particular, we use various versions of these numbers to discuss methods of derivation of quantum spectral curves from the point of view of KP integrability and derive new examples of quantum curves for the families of double Hurwitz numbers.
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