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arXiv · 1511.02860

Exact quantization conditions for the relativistic Toda lattice

Yasuyuki Hatsuda·Marcos Marino
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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.

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Yasuyuki Hatsuda, Marcos Marino. 2020-01-09. Exact quantization conditions for the relativistic Toda lattice. https://doi.org/10.1007/jhep05(2016)133

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