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Deforming SW curve

A system of Bethe-Ansatz type equations, which specify a unique array of Young tableau responsible for the leading contribution to the Nekrasov partition function in the $ε_2\rightarrow 0$ limit is derived. It is shown that the prepotential with generic $ε_1$ is directly related to the (rescaled by $ε_1$) number of total boxes of these Young tableau. Moreover, all the expectation values of the chiral fields $\langle \tr ϕ^J \rangle $ are simple symmetric functions of their column lengths. An entire function whose zeros are determined by the column lengths is introduced. It is shown that this function satisfies a functional equation, closely resembling Baxter's equation in 2d integrable models. This functional relation directly leads to a nice generalization of the equation defining Seiberg-Witten curve.