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

Abstract We consider the Seiberg-Witten solution of pure N $$ \mathcal{N} $$ = 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 a I (u), a DI (u) on the N − 1 Coulomb-branch moduli u n is obtained around the ℤ2N -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 Kähler potential K = 1 2 ∑ I $$ \frac{1}{2}{\sum}_I $$ Im( a ¯ $$ \overline{a} $$ I a DI ), 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.