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The AGT conjecture relates \mathcal{N}=2 4d SUSY gauge theories to 2d CFTs.Matrix model techniques can be used to investigate both sides of this relation.The large N limit refers here to the size of Young tableaux in the expressionof the gauge theory partition function. It corresponds to the vanishing ofOmega-background equivariant deformation parameters, and should not be confusedwith the t'Hooft expansion at large number of colors. In this paper, a saddlepoint approach is employed to study the Nekrasov-Shatashvili limit of the gaugetheory, leading to define beta-deformed, or quantized, Seiberg-Witten curve anddifferential form. Then this formalism is compared to the large N limit of theDijkgraaf-Vafa beta-ensemble. A transformation law relating the wave functionsappearing at both sides of the conjecture is proposed. It implies atransformation of the Seiberg-Witten 1-form in agreement with the definitionspecified earlier. As a side result, a remarkable property of \mathcal{N}=2theories emerged: the instanton contribution to the partition function can bedetermined from the perturbative term analysis.

Large N techniques for Nekrasov partition functions and AGT conjecture