English

Exact quantization conditions for cluster integrable systems

High Energy Physics - Theory 2016-08-03 v2 Mathematical Physics math.MP Spectral Theory Exactly Solvable and Integrable Systems

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.

Keywords

Cite

@article{arxiv.1512.03061,
  title  = {Exact quantization conditions for cluster integrable systems},
  author = {Sebastian Franco and Yasuyuki Hatsuda and Marcos Marino},
  journal= {arXiv preprint arXiv:1512.03061},
  year   = {2016}
}

Comments

27 pages, v2: published version

R2 v1 2026-06-22T12:05:48.271Z