  We study the beta-ensemble that represents conformal blocks of Liouville
theory on the sphere. This quantity is related through AGT conjecture to the
Nekrasov instanton partition function of 4d $\mathcal{N}=2$ SU(2) gauge theory
with four flavors. We focus on the large N limit, equivalent to the
Nekrasov-Shatashvili limit where one of the Omega-background deformation
parameters is vanishing. A quantized Seiberg-Witten differential form is
defined perturbatively in h-bar as the singular part of the beta-ensemble
resolvent. Using the Dyson collective field action, we show that the free
energy obeys the Seiberg-Witten relations. As suggested by Mironov and Morozov,
the quantized differential form can be obtained from the classical one by the
action of a differential operator in the hypermultiplet masses and the Coulomb
branch modulus.
