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Exact quantization conditions for cluster integrable systems (1512.03061v2)
Published 9 Dec 2015 in hep-th, math-ph, math.MP, math.SP, and nlin.SI
Abstract: We propose exact quantization conditions for the quantum integrable systems of Goncharov and Kenyon, based on the enumerative geometry of the corresponding toric Calabi-Yau manifolds. Our conjecture builds upon recent results on the quantization of mirror curves, and generalizes a previous proposal for the quantization of the relativistic Toda lattice. We present explicit tests of our conjecture for the integrable systems associated to the resolved C3/Z_5 and C3/Z_6 orbifolds.