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Conformal blocks as Dotsenko-Fateev Integral Discriminants

As anticipated in [1], elaborated in [2-4], and explicitly formulated in [5], the Dotsenko-Fateev integral discriminant coincides with conformal blocks, thus providing an elegant approach to the AGT conjecture, without any reference to an auxiliary subject of Nekrasov functions. Internal dimensions of conformal blocks in this identification are associated with the choice of contours: parameters of the DV phase of the corresponding matrix models. In this paper we provide further evidence in support of this identity for the 6-parametric family of the 4-point spherical conformal blocks, up to level 3 and for arbitrary values of external dimensions and central charges. We also extend this result to multi-point spherical functions and comment on a similar description of the 1-point function on a torus.