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

• Published in: The journal of high energy physics 2022-11, Vol.2022 (11), p.102-55, Article 102
• Main Authors: D’Hoker, Eric, Dumitrescu, Thomas T., Nardoni, Emily
• Format: Article
• Language: English
• Subjects: Classical and Quantum Gravitation; Elementary Particles; Gauge theory; High energy physics; Hypergeometric functions; Integrable Field Theories; Integrals; Physics; Physics and Astronomy; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Series expansion; String Theory; Supersymmetric Effective Theories; Supersymmetric Gauge Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP11(2022)102

A bstract 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 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 = 1 2 ∑ I Im( 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.