2015/11/30 by Yasuyuki Hatsuda, Marcos Marino · 1 citation
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.MP #math.SP
paper · pdf · doi:10.1007/jhep05(2016)133
31pages, v2: misprints corrected, references added, v3: published version, v4: typo in eq.(2.49) fixed
arxiv created 2020/01/09 · arxiv updated 2020/01/15
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.