Charlie Dworaczek Guera: The sinh-model: Quantum separation of variables and Lukyanov’s conjecture

Abstract:

The quantum separation of variables method developed by Sklyanin in 1985 serves as an alternative to Algebraic Bethe Ansatz which doesn’t apply to quantum integrable models without so-called pseudo-vacuum state such as the quantum Toda chain. This method allows to express some quantities of interests of these models (spectrum, eigenstates, matrix elements…) as \(N\)-fold multiple integrals (or at least some of its building blocks) for which one would be interested in obtaining the \(N\)-asymptotic expansion. These integrals are similar to the partition functions of β-ensembles with non-varying weights (without a scaling in \(N\) for the potential) and with a log sinh interaction instead of a log interaction. Due to these features, the study of these integrals is highly technical and were studied partly in [Borot, Guionnet, Kozlowski 16’] and [D-G, Kozlowski 24’]. I will present the model in this talk and demonstrate how a biorthogonal approach can contribute to a progress on Lukyanov’s conjecture about sinh-Gordon QFT. This is a joint work with Karol K. Kozlowski.