  Once famous and a little mysterious, AGT relations between Nekrasov functions
and conformal blocks are now understood as the Hubbard-Stratanovich duality in
the Dijkgraaf-Vafa (DV) phase of a peculiar Dotsenko-Fateev multi-logarithmic
matrix model. However, it largely remains a collection of somewhat technical
tricks, lacking a clear and generalizable conceptual interpretation. Our new
claim is that the Nekrasov functions emerge in matrix models as a
straightforward implication of superintegrability, factorization of peculiar
matrix model averages. Recently, we demonstrated that, in the Gaussian
Hermitian model, the factorization property can be extended from averages of
single characters to their bilinear combinations. In this paper, we claim that
this is true also for multi-logarithmic matrix models, where factorized are
just the point-split products of two characters. It is this enhanced
superintegrability that is responsible for existence of the Nekrasov functions
and the AGT relations. This property can be generalized both to multi-matrix
models, thus leading to AGT relations for multi-point conformal blocks, and to
DV phases of other non-Gaussian models.
