Unoriented Strings, Loop Equations, and N=1 Superpotentials from Matrix Models

Abstract

We apply the proposal of Dijkgraaf and Vafa to analyze N=1 gauge theory with SO(N) and Sp(N) gauge groups with arbitrary tree-level superpotentials using matrix model techniques. We derive the planar and leading non-planar contributions to the large M SO(M) and Sp(M) matrix model free energy by applying the technology of higher-genus loop equations and by straightforward diagrammatics. The loop equations suggest that the RP^2 free energy is given as a derivative of the sphere contribution, a relation which we verify diagrammatically. With a refinement of the proposal of Dijkgraaf and Vafa for the effective superpotential, we find agreement with field theory expectations.

LaTeX, 41 pages, 1 figure, 1 C source file. References added. Derivation of loop equation corrected; result for free energy unchanged

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Cited by in corpus (37)

• An Introduction to Supersymmetric Gauge Theories and Matrix Models
• Matrix model approach to the N=2 U(N) gauge theory with matter in the fundamental representation
• Holomorphic matrix models
• Unified description of correlators in non-Gaussian phases of Hermitean matrix model
• On the Matter of the Dijkgraaf--Vafa Conjecture
• (Anti)symmetric matter and superpotentials from IIB orientifolds
• On Low Rank Classical Groups in String Theory, Gauge Theory and Matrix Models
• Exact probes of orientifolds
• Effective Superpotentials via Konishi Anomaly
• Loop equations, matrix models, and N=1 supersymmetric gauge theories
• Multi-Trace Superpotentials vs. Matrix Models
• Super Yang-Mills With Flavors From Large N_f Matrix Models
• Constructing Gauge Theory Geometries from Matrix Models
• Cubic curves from matrix models and generalized Konishi anomalies
• Exact Mesonic Vacua From Matrix Models
• Matrix-model description of N=2 gauge theories with non-hyperelliptic Seiberg-Witten curves
• On the property of Cachazo-Intriligator-Vafa prepotential at the extremum of the superpotential
• Chern-Simons Matrix Models and Unoriented Strings
• Chiral field theories from conifolds
• Note on Matrix Model with Massless Flavors
• Chiral field theories, Konishi anomalies and matrix models
• Universality and asymptotics of graph counting problems in nonorientable surfaces
• Phases of N=1 SO(N_c) Gauge Theories with Flavors
• N=2 Supersymmetric SO(N)/Sp(N) Gauge Theories from Matrix Model
• The Glueball Superpotential
• Improved matrix-model calculation of the N=2 prepotential
• Gravitational F-terms of SO/Sp gauge theories and anomalies
• Wilson loops in $\mathcal{N}=4$ $SO(N)$ SYM and D-Branes in $Ad{S}_5\times {\mathbb{RP}}^5$
• {\cal N}=2 SO(N) SYM theory from Matrix Model
• Konishi Anomalies and Curves without Adjoints
• Chiral rings, anomalies and loop equations in N=1* gauge theories
• Effective superpotential for U(N) with antisymmetric matter
• The Matrix Model Curve Near the Singularities
• Effective Potentials and the Vacuum Structure of Quantum Field Theories
• Aspects of Supersymmetric Gauge Theory and String Theory
• Exact Effective Superpotential for SO(N_c) Gauge Theory with $N_f$ Flavors
• Effective SO Superpotential for N=1 Theory with N_f Fundamental Matter