Deforming SW curve

Details Deforming SW curve Deforming SW curve

2010-06-24

arxiv.org/abs/1006.4822v1

JHEP 1104:033,2011

Physics

High Energy Physics

High Energy Physics - Theory

14 pages

Scientific paper

10.1007/JHEP04(2011)033

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. 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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