Exploring the strong-coupling region of SU(N) Seiberg-Witten theory

We consider the Seiberg-Witten solution of pure 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 alpha(I)(u), alpha(DI)(u) on the N-1 Coulomb-branch moduli u(n) is obtained around the Z(2N)-symmetric point of the Coulomb branch, where all u(n) 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 Kahler potential K = 1/2 pi Sigma(I) Im((alpha) over bar alpha(DI)) which is single valued on the Coulomb branch. Evidence is presented that K is a convex function, with a unique minimum at the Z(2N)-symmetric point. Finally, we explore candidate walls of marginal stability in the vicinity of this point, and their relation to the surface of vanishing Kahler potential.