Nekrasov functions and exact Bohr-Sommerfeld integrals

By A. Mironov, A. Morozov. 2009

342 citations recorded by the source corpus.

In the case of SU(2), associated by the AGT relation to the 2d Liouville theory, the Seiberg-Witten prepotential is constructed from the Bohr-Sommerfeld periods of 1d sine-Gordon model. If the same construction is literally applied to monodromies of exact wave functions, the prepotential turns into the one-parametric Nekrasov prepotential $$\mathcal{F} (a, \epsilon_{1}) $$ with the other epsilon parameter vanishing, ϵ2 = 0, and ϵ1 playing the role of the Planck constant in the sine-Gordon Shrödinger equation, ℏ = ϵ1. This seems to be in accordance with the recent claim in [1] and poses a problem of describing the full Nekrasov function as a seemingly straightforward double-parametric quantization of sine-Gordon model. This also provides a new link between the Liouville and sine-Gordon theories.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/24a01f5089e6fb31ebd4dc168223a93092b67a46

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

The Ω Deformed B-model for Rigid N = 2 Theories (2011, background): “6) [88] [γ(∂(2) E + ∂ 2 γ) + 2E∂E∂γ ]Π (0) = 0 .”
Topological Strings from Quantum Mechanics (2014, background): “Inspired by the work of [13], it was found in [16–18] that the perturbative WKB quantization condition for the spectrum of these operators is closely related to the NS limit of the refined topological string on X.”
Quantum geometry of refined topological strings (2011, background): “For example, this idea has been put forward in the gauge theory context in [60].”
Non-perturbative effects and the refined topological string (2013, background): “In [17, 18], Mironov and Morozov interpreted the quantization in terms of quantum periods of the spectral curve describing the integrable system.”