Cubic curves from matrix models and generalized Konishi anomalies

Abstract

We study the matrix model/gauge theory connection for three different N=1 models: U(N) x U(N) with matter in bifundamental representations, U(N) with matter in the symmetric representation, and U(N) with matter in the antisymmetric representation. Using Ward identities, we explicitly show that the loop equations of the matrix models lead to cubic algebraic curves. We then establish the equivalence of the matrix model and gauge theory descriptions in two ways. First, we derive generalized Konishi anomaly equations in the gauge theories, showing that they are identical to the matrix-model equations. Second, we use a perturbative superspace analysis to establish the relation between the gauge theories and the matrix models. We find that the gauge coupling matrix for U(N) with matter in the symmetric or antisymmetric representations is_not_ given by the second derivative of the matrix-model free energy. However, the matrix-model prescription can be modified to give the gauge coupling matrix.

27 pages, 2 figures; v2: minor corrections and clarifications; v3: published version

References in corpus (24)

• Chiral Rings and Anomalies in Supersymmetric Gauge Theory
• A Perturbative Window into Non-Perturbative Physics
• Perturbative Computation of Glueball Superpotentials
• Phases of N=1 Supersymmetric Gauge Theories and Matrices
• Chiral Rings and Phases of Supersymmetric Gauge Theories
• Quantum parameter space and double scaling limits in N=1 super Yang-Mills theory
• Matrix model approach to the N=2 U(N) gauge theory with matter in the fundamental representation
• Holomorphic matrix models
• Adding Fundamental Matter to ``Chiral Rings and Anomalies in Supersymmetric Gauge Theory''
• The N=2 gauge theory prepotential and periods from a perturbative matrix model calculation
• Unoriented Strings, Loop Equations, and N=1 Superpotentials from Matrix Models
• Perturbative Computation of Glueball Superpotentials for SO(N) and USp(N)
• Konishi anomaly and N=1 effective superpotentials from matrix models
• On the Matter of the Dijkgraaf--Vafa Conjecture
• SO(N) Superpotential, Seiberg-Witten Curves and Loop Equations
• (Anti)symmetric matter and superpotentials from IIB orientifolds
• Phases of N=1 Supersymmetric Gauge Theories with Flavors
• Multi-Trace Superpotentials vs. Matrix Models
• $\mathcal{N}=1$ Theories and a Geometric Master Field
• Derivation of the Konishi anomaly relation from Dijkgraaf-Vafa with (Bi-)fundamental matters
• Super Yang-Mills With Flavors From Large N_f Matrix Models
• Phases of N=1 Supersymmetric SO/Sp Gauge Theories via Matrix Model
• Constructing Gauge Theory Geometries from Matrix Models
• Note on Matrix Model with Massless Flavors

Cited by in corpus (18)

• An A_r threesome: Matrix models, 2d CFTs and 4d N=2 gauge theories
• (Anti)symmetric matter and superpotentials from IIB orientifolds
• On Low Rank Classical Groups in String Theory, Gauge Theory and Matrix Models
• N=1 Geometries via M-theory
• Branches of N=1 Vacua and Argyres-Douglas Points
• Matrix-model description of N=2 gauge theories with non-hyperelliptic Seiberg-Witten curves
• Phases and geometry of the N=1 A_2 quiver gauge theory and matrix models
• Chiral field theories, Konishi anomalies and matrix models
• Irregular conformal block, spectral curve and flow equations
• Quivers via anomaly chains
• Improved matrix-model calculation of the N=2 prepotential
• An Exact Relation for N=1 Orientifold Field Theories with Arbitrary Superpotential
• Remarks on the analytic structure of supersymmetric effective actions
• More on N=1 Matrix Model Curve for Arbitrary N
• Konishi Anomalies and Curves without Adjoints
• Effective superpotential for U(N) with antisymmetric matter
• Quantum Geometries of $A_2$
• Grand Pleromal Transmutation : condensates via Konsishi anomaly, dimensional transmutation and ultraminimal GUTs