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Scientific article
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English

Exact quantization conditions for the relativistic Toda lattice

Published inThe journal of high energy physics, vol. 1605, p. 133-168
Collection
  • Open Access - SCOAP3
Publication date2016
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 Strings
  • Lattice Integrable Models
  • Nonperturbative Effects
Citation (ISO format)
HATSUDA, Yasuyuki, MARINO BEIRAS, Marcos. Exact quantization conditions for the relativistic Toda lattice. In: The journal of high energy physics, 2016, vol. 1605, p. 133–168. doi: 10.1007/JHEP05(2016)133
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Article (Published version)
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ISSN of the journal1029-8479
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