Loop equations, matrix models, and N=1 supersymmetric gauge theories

Abstract

We derive the Konishi anomaly equations for N=1 supersymmetric gauge theories based on the classical gauge groups with matter in two-index tensor and fundamental representations, thus extending the existing results for U(N). A general formula is obtained which expresses solutions to the Konishi anomaly equation in terms of solutions to the loop equations of the corresponding matrix model. This provides an alternative to the diagrammatic proof that the perturbative part of the glueball superpotential $W_{\mathrm{eff}}$ for these matter representations can be computed from matrix model integrals, and further shows that the two approaches always give the same result. The anomaly approach is found to be computationally more efficient in the cases we studied. Also, we show in the anomaly approach how theories with a traceless two-index tensor can be solved using an associated theory with a traceful tensor and appropriately chosen coupling constants.

27 pages, amstex, no figures. v2: references added. v3: minor corrections

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Cited by in corpus (23)

• The uses of the refined matrix model recursion
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• Konishi anomaly approach to gravitational F-terms
• Supersymmetric Gauge Theories with Flavors and Matrix Models
• Chern-Simons Matrix Models and Unoriented Strings
• Chiral field theories from conifolds
• Phases and geometry of the N=1 A_2 quiver gauge theory and matrix models
• Chiral field theories, Konishi anomalies and matrix models
• On Nonperturbative Exactness of Konishi Anomaly and the Dijkgraaf-Vafa Conjecture
• Gravitational F-terms through anomaly equations and deformed chiral rings
• Improved matrix-model calculation of the N=2 prepotential
• The Affine Connection of Supersymmetric SO(N)/Sp(N) Theories
• Chiral SU(N) Gauge Theories and the Konishi Anomaly
• Gravitational F-terms of SO/Sp gauge theories and anomalies
• An Exact Relation for N=1 Orientifold Field Theories with Arbitrary Superpotential
• More on N=1 Matrix Model Curve for Arbitrary N
• Effective superpotential for U(N) with antisymmetric matter
• Konishi Anomalies and Curves without Adjoints
• Chiral rings, anomalies and loop equations in N=1* gauge theories
• On the Chiral Ring of N=1 Supersymmetric Gauge Theories
• Dual Interpretations of Seiberg-Witten and Dijkgraaf-Vafa curves