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- W4299673954 abstract "We propose that the grand canonical topological string partition functions satisfy finite-difference equations in the closed string moduli. In the case of genus one mirror curve these are conjectured to be the q-difference Painlev'e equations as in Sakai's classification. More precisely, we propose that the tau-functions of q-Painlev'e equations are related to the grand canonical topological string partition functions on the corresponding geometry. In the toric cases we use topological string/spectral theory duality to give a Fredholm determinant representation for the above tau-functions in terms of the underlying quantum mirror curve. As a consequence, the zeroes of the tau-functions compute the exact spectrum of the associated quantum integrable systems. We provide details of this construction for the local $mathbb{P}^1times mathbb{P}^1$ case, which is related to q-difference Painlev'e with affine $A_1$ symmetry, to $SU(2)$ Super Yang-Mills in five dimensions and to relativistic Toda system." @default.
- W4299673954 created "2022-10-02" @default.
- W4299673954 creator A5024536407 @default.
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- W4299673954 date "2017-10-31" @default.
- W4299673954 modified "2023-10-16" @default.
- W4299673954 title "Quantum curves and $q$-deformed Painlev'e equations" @default.
- W4299673954 doi "https://doi.org/10.48550/arxiv.1710.11603" @default.
- W4299673954 hasPublicationYear "2017" @default.
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