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arXiv · 1512.03061

Exact quantization conditions for cluster integrable systems

Sebastian Franco·Yasuyuki Hatsuda·Marcos Marino
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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 C^3/Z_5 and C^3/Z_6 orbifolds.

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Sebastian Franco, Yasuyuki Hatsuda, Marcos Marino. 2015-12-09. Exact quantization conditions for cluster integrable systems. https://doi.org/10.1088/1742-5468%2F2016%2F06%2F063107

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