Nekrasov functions and exact Bohr-Sommerfeld integrals

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 F(a, epsilon(1)) with the other epsilon parameter vanishing, epsilon(2) = 0, and epsilon(1) playing the role of the Planck constant in the sine-Gordon Shrodinger equation, (h) over bar = epsilon(1). 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.