Exploring the Strong-Coupling Region of $SU(N)$ Seiberg-Witten Theory

Abstract

We consider the Seiberg-Witten solution of pure $\mathcal{N}=2$ 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 ${\mathbb{Z}}_{2N}$-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 Kähler potential $K=\frac{1}{2\pi }{\sum }_I\text{Im}({\bar{a}}_I{a}_{DI})$, which is single valued on the Coulomb branch. Evidence is presented that $K$ is a convex function, with a unique minimum at the ${\mathbb{Z}}_{2N}$-symmetric point. Finally, we explore candidate walls of marginal stability in the vicinity of this point, and their relation to the surface of vanishing Kähler potential.

arXiv comment68 pages

References in corpus (24)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• New Phenomena in SU(3) Supersymmetric Gauge Theory
• Simple Singularities and N=2 Supersymmetric Yang-Mills Theory
• The Vacuum Structure and Spectrum of N=2 Supersymmetric SU(N) Gauge Theory
• Dynamics of $SU(N)$ Supersymmetric Gauge Theory
• Introduction to S-Duality in N=2 Supersymmetric Gauge Theory. (A pedagogical review of the work of Seiberg and Witten)
• Comments on Supercurrent Multiplets, Supersymmetric Field Theories and Supergravity
• Nonperturbative Effective Actions of N=2 Supersymmetric Gauge Theories
• The Strong-Coupling Spectrum of the Seiberg-Witten Theory
• Supercurrents and Brane Currents in Diverse Dimensions
• The Effective Prepotential of N=2 Supersymmetric SU(N_c) Gauge Theories
• Soft Supersymmetry Breaking in Deformed Moduli Spaces, Conformal Theories, and N = 2 Yang-Mills Theory
• The Renormalization Group Equation in N=2 Supersymmetric Gauge Theories
• Wild Wall Crossing and BPS Giants
• Prepotentials in N=2 SU(2) Supersymmetric Yang-Mills Theory with Massless Hypermultiplets
• Strong Coupling Expansions of SU(N) Seiberg-Witten Theory
• A New Derivation of the Picard-Fuchs Equations for Effective $N=2$ Super Yang-Mills Theories
• On the Picard-Fuchs equations of the SW models
• Strong coupling expansion and Seiberg-Witten-Whitham equations
• Prepotential of $N=2$ Supersymmetric Yang-Mills Theories in the Weak Coupling Region
• On The Strong-Coupling Spectrum of Pure SU(3) Seiberg-Witten Theory
• N=2 supersymmetric Yang-Mills theories and Whitham integrable hierarchies
• On the Moduli Space of SU(3) Seiberg-Witten Theory with Matter

Cited by in corpus (1)

• Candidate Phases for SU(2) Adjoint QCD${}_4$ with Two Flavors from $\mathcal{N}=2$ Supersymmetric Yang-Mills Theory