Exact quantization conditions for cluster integrable systems

Wednesday, 9 December, 2015

Published in: 

arXiv:1512.03061

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.

Author(s): 

Sebastian Franco
Yasuyuki Hatsuda
Marcos Marino