Deforming SW curve

Understand

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 $\epsilon_2\rightarrow 0$ limit is derived.

• It is shown that the prepotential with generic $\epsilon_1$ is directly related to the (rescaled by $\epsilon_1$) number of total boxes of these Young tableau.
• Moreover, all the expectation values of the chiral fields $\langle \tr \phi^J \rangle $ are simple symmetric functions of their column lengths.
• An entire function whose zeros are determined by the column lengths is introduced.