Abstract
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.
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ArXiv ePrint: 0910.5670v2
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Mironov, A., Morozov, A. Nekrasov functions and exact Bohr-Sommerfeld integrals. J. High Energ. Phys. 2010, 40 (2010). https://doi.org/10.1007/JHEP04(2010)040
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DOI: https://doi.org/10.1007/JHEP04(2010)040