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.

Automated summary

This paper discusses the Seiberg-Witten solution of pure N = 2 gauge theory in four dimensions, obtaining an exact series expansion for the dependence of Seiberg-Witten periods on Coulomb-branch moduli. The global structure of the Kahler potential on the Coulomb branch is explored utilizing analytical results and numerical computations.