Deformed SW curve and the null vector decoupling equation in Toda field theory

It is shown that the deformed seiberg-witten curve equation after fourier transform is mapped into a differential equation for the agt dual 2d cft cnformal block containing an extra completely degenerate field. we carefully match parameters in two sides of duality thus providing not only a simple independent prove of the agt correspondence in nekrasov-shatashvili limit, but also an extension of agt to the case when a secondary field is included in the cft conformal block. implications of our results in the study of monodromy problems for a large class of n’th order fuchsian differential equations are discussed.