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Title: Exploring the strong-coupling region of SU(N) Seiberg-Witten theory
A bstract We consider the Seiberg-Witten solution of pure $$ \mathcal{N} $$ 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 ℤ 2 N -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 = $$ \frac{1}{2}{\sum}_I $$ 1 2 ∑ I Im( $$ \overline{a} $$ 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 ℤ 2 N -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.  more » « less
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Journal of High Energy Physics
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National Science Foundation
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