Abstract
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 ϵ2 → 0 limit is derived. It is shown that the prepotential with generic ϵ1 is directly related to the (rescaled by ϵ2) number of total boxes of these Young tableau. Moreover, all the expectation values of the chiral fields $ \left\langle {{\text{tr}}{\phi^J}} \right\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.
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