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Exact quantization conditions for the relativistic Toda lattice

Published in Journal of High Energy Physics. 2016, vol. 1605, p. 133-168
Collection Open Access - SCOAP3
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 Topological StringsLattice Integrable ModelsNonperturbative Effects
arXiv: 1511.02860
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HATSUDA, Yasuyuki, MARINO BEIRAS, Marcos. Exact quantization conditions for the relativistic Toda lattice. In: Journal of High Energy Physics, 2016, vol. 1605, p. 133-168. https://archive-ouverte.unige.ch/unige:84168

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Deposited on : 2016-06-03

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