Abstract
We consider the Seiberg-Witten solution of pure mathcal{N} = 2 gauge theory in four dimensions, with gauge group SU(N). A simple exact series expansion for the dependence of the 2(N − 1) Seiberg-Witten periods aI(u), aDI(u) on the N − 1 Coulomb-branch moduli un is obtained around the ℤ2N-symmetric point of the Coulomb branch, where all un vanish. This generalizes earlier results for N = 2 in terms of hypergeometric functions, and for N = 3 in terms of Appell functions. Using these and other analytical results, combined with numerical computations, we explore the global structure of the Kähler potential K = frac{1}{2}{sum}_I Im( overline{a} IaDI), which is single valued on the Coulomb branch. Evidence is presented that K is a convex function, with a unique minimum at the ℤ2N-symmetric point. Finally, we explore candidate walls of marginal stability in the vicinity of this point, and their relation to the surface of vanishing Kähler potential.
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