The Vacuum Structure of N=2 SuperQCD with Classical Gauge Groups

Abstract

We determine the vacuum structure of N=2 supersymmetric QCD with fundamental quarks for gauge groups SO(n) and Sp(2n), extending prior results for SU(n). The solutions are all given in terms of families of hyperelliptic Riemann surfaces of genus equal to the rank of the gauge group. In the scale invariant cases, the solutions all have exact S-dualities which act on the couplings by subgroups of PSL(2,Z) and on the masses by outer automorphisms of the flavor symmetry. They are shown to reproduce the complete pattern of symmetry breaking on the Coulomb branch and predict the correct weak--coupling monodromies. Simple breakings with squark vevs provide further consistency checks involving strong--coupling physics.

29 pages, harvmac, 1 figure included using epsf.tex

References in corpus (11)

• New Phenomena in SU(3) Supersymmetric Gauge Theory
• Simple Singularities and N=2 Supersymmetric Yang-Mills Theory
• Integrability and Seiberg-Witten Exact Solution
• The Vacuum Structure and Spectrum of N=2 Supersymmetric SU(N) Gauge Theory
• Integrable systems and supersymmetric gauge theory
• The Coulomb Phase of N=2 Supersymmetric QCD
• Dynamics of $SU(N)$ Supersymmetric Gauge Theory
• Duality, Monopoles, Dyons, Confinement and Oblique Confinement in Supersymmetric SO(N_c) Gauge Theories
• On the Monodromies of N=2 Supersymmetric Yang-Mills Theory with Gauge Group SO(2n)
• Whitham-Toda hierarchy and N = 2 supersymmetric Yang-Mills theory
• On the Monodromies of N=2 Supersymmetric Yang-Mills Theory

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