Exact quantization conditions for cluster integrable systems. (29th June 2016)

• Record Type: Journal Article
• Authors: Franco, Sebastián; Hatsuda, Yasuyuki; Mariño, Marcos
• Is Part Of: Journal of statistical mechanics. (2016:Jun.)
• Publication Date: 2016-06-29
• Subjects: Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/2016/06/063107
• Languages: English
• ISSNs: 1742-5468

Abstract

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.