Chiral Rings, Vacua and Gaugino Condensation of Supersymmetric Gauge Theories

Abstract

We find the complete chiral ring relations of the supersymmetric U(N) gauge theories with matter in adjoint representation. We demonstrate exact correspondence between the solutions of the chiral ring and the supersymmetric vacua of the gauge theory. The chiral ring determines the expectation values of chiral operators and the low energy gauge group. All the vacua have nonzero gaugino condensation. We study the chiral ring relations obeyed by the gaugino condensate. These relations are generalizations of the formula $S^N={\Lambda }^{3N}$ of the pure $\mathcal{N}=1$ gauge theory.

arXiv comment38 pages

References in corpus (6)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Chiral Rings and Anomalies in Supersymmetric Gauge Theory
• A Large N Duality via a Geometric Transition
• Dynamics of $SU(N)$ Supersymmetric Gauge Theory
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Cited by in corpus (7)

• Counting chiral primaries in N=1 d=4 superconformal field theories
• The Chiral Ring and the Periods of the Resolvent
• On Nonperturbative Exactness of Konishi Anomaly and the Dijkgraaf-Vafa Conjecture
• Finiteness of Flux Vacua from Geometric Transitions
• Effective superpotential for U(N) with antisymmetric matter
• Sp(N) higher-derivative F-terms via singular superpotentials
• Low Energy Effective Action in N=2 Yang-Mills as an Integrated Anomaly