Whitham Deformations of Seiberg-Witten Curves for Classical Gauge Groups

Details Whitham Deformations of Seiberg-Witten Curves for Classical Gauge Groups Whitham Deformations of Seiberg-Witten Curves for Classical Gauge Groups

1999-01-25

arxiv.org/abs/hep-th/9901120v2

Int.J.Mod.Phys. A15 (2000) 3635-3666

Physics

High Energy Physics

High Energy Physics - Theory

latex, 39pp, no figure; some more comments and references on integrable systems are added, and many typos are corrected

Scientific paper

10.1142/S0217751X00002364

Gorsky et al. presented an explicit construction of Whitham deformations of the Seiberg-Witten curve for the $SU(N+1)$ $\calN = 2$ SUSY Yang-Mills theory. We extend their result to all classical gauge groups and some other cases such as the spectral curve of the $A^{(2)}_{2N}$ affine Toda Toda system. Our construction, too, uses fractional powers of the superpotential $W(x)$ that characterizes the curve. We also consider the $u$-plane integral of topologically twisted theories on four-dimensional manifolds $X$ with $b_2^{+}(X) = 1$ in the language of these explicitly constructed Whitham deformations and an integrable hierarchy of the KdV type hidden behind.

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