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$Q$-functions for lambda opers

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arxiv 2312.08842 v3 pith:74N23L6R submitted 2023-12-14 math-ph math.MPmath.QA

Davide Masoero , Evgeny Mukhin , Andrea Raimondo This is my paper
classification math-phmath.MPmath.QA
keywords functionsoperslambdaconjectureansatzbazhanov-lukyanov-zamolodchikovbethecalled
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abstract

We consider the Schr\"odinger operators which are constructed from the $\lambda$-opers corresponding to solutions of the $\widehat{\mathfrak{sl}}_2$ Gaudin Bethe Ansatz equations. We define and study the connection coefficients called the $Q$-functions. We conjecture that the $Q$-functions obtained from the $\lambda$-opers coincide with the $Q$-functions of the Bazhanov-Lukyanov-Zamolodchikov opers with the monster potential related to the quantum KdV flows. We give supporting evidence for this conjecture.

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  1. On W-algebras and ODE/IM correspondence

    hep-th 2025-08 conditional novelty 6.0 of 10

    The eigenvalues of quantum KdV-type charges in Virasoro, W3, and W4 algebras are computed from Bethe roots via WKB periods of Catalan curves, verified against direct CFT diagonalization.

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