Dequantization conjecture for quantum spectral curves

Let W{\mathcal W} be a point of the Sato Grassmannian with wave function Ψ\Psi and quantum spectral curve operator PW{\mathtt P}_{\mathcal W}, so that

PWΨ=0.{\mathtt P}_{\mathcal W}\cdot\Psi=0.

For a tau-function with a genus or topological expansion, conjugate this equation by the unstable contributions and take its semi-classical limit. Quantum spectral curve conjecture. The resulting semi-classical limit should lead to the classical spectral curve. In this approach the classical spectral curve is obtained by dequantizing the quantum spectral curve, which is therefore regarded as more fundamental. The claim is presented as an expectation and the source gives no resolution status; it is described as consistent with concepts in the literature.

Sources & referencesView supporting material

Primary source

Alexander Alexandrov, “KP integrability of triple Hodge integrals. II. Generalized Kontsevich matrix model”, arXiv:2009.10961 (2021).

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