Exact quantization conditions for the relativistic Toda lattice
Abstract
Inspired by recent connections between spectral theory and topological string theory, we propose exact quantization conditions for the relativistic Toda lattice of N particles. These conditions involve the Nekrasov-Shatashvili free energy, which resums the perturbative WKB expansion, but they require in addition a non-perturbative contribution, which is related to the perturbative result by an S-duality transformation of the Planck constant. We test the quantization conditions against explicit calculations of the spectrum for N=3. Our proposal can be generalized to arbitrary toric Calabi-Yau manifolds and might solve the corresponding quantum integrable system of Goncharov and Kenyon.
Keywords
Cite
@article{arxiv.1511.02860,
title = {Exact quantization conditions for the relativistic Toda lattice},
author = {Yasuyuki Hatsuda and Marcos Marino},
journal= {arXiv preprint arXiv:1511.02860},
year = {2020}
}
Comments
31pages, v2: misprints corrected, references added, v3: published version, v4: typo in eq.(2.49) fixed