An Introduction to Supersymmetric Gauge Theories and Matrix Models

Abstract

We give an introduction to the recently established connection between supersymmetric gauge theories and matrix models. We begin by reviewing previous material that is required in order to follow the latest developments. This includes the superfield formulation of gauge theories, holomorphy, the chiral ring, the Konishi anomaly and the large N limit. We then present both the diagrammatic proof of the connection and the one based on the anomaly. Our discussion is entirely field theoretical and self contained.

78 pages, 7 figures, 2 tables, V2: eq. (148) corrected; minor changes in Sect. 5; 2 Refs. added, V3: 1 Ref added, V4: eqs. (126) and (257) corrected

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• Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories
• Exact Results on the Space of Vacua of Four Dimensional SUSY Gauge Theories
• Exactly Marginal Operators and Duality in Four Dimensional N=1 Supersymmetric Gauge Theory
• New Phenomena in SU(3) Supersymmetric Gauge Theory
• Superstrings and Topological Strings at Large N
• The String Dual of a Confining Four-Dimensional Gauge Theory
• Chiral Rings and Anomalies in Supersymmetric Gauge Theory
• A Perturbative Window into Non-Perturbative Physics
• Naturalness Versus Supersymmetric Non-renormalization Theorems
• The Calculus of Many Instantons
• Worldsheet Derivation of a Large N Duality
• Exact Superpotentials in Four Dimensions
• Spectrum of Type IIB Supergravity on AdS_5 x T^{11}: Predictions on N = 1 SCFT's
• Varieties of vacua in classical supersymmetric gauge theories
• INSTANTON CALCULATIONS VERSUS EXACT RESULTS IN 4 DIMENSIONAL SUSY GAUGE THEORIES.
• Perturbative Computation of Glueball Superpotentials
• Perturbative Analysis of Gauged Matrix Models
• ``Integrating in'' and exact superpotentials in 4d
• Exact Superpotentials for Theories with Flavors via a Matrix Integral
• N=1 Supersymmetry, Deconstruction, and Bosonic Gauge Theories
• Quantum parameter space and double scaling limits in N=1 super Yang-Mills theory
• On exact superpotentials in confining vacua
• Quantum moduli spaces from matrix models
• 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
• Konishi anomaly and N=1 effective superpotentials from matrix models
• On the Quantum Moduli Space of M Theory Compactifications
• (Anti)symmetric matter and superpotentials from IIB orientifolds
• Baryons, Boundaries and Matrix Models
• Perturbative Derivation of Exact Superpotential for Meson Fields from Matrix Theories with One Flavour
• Baryonic Corrections to Superpotentials from Perturbation Theory
• Seiberg Duality in Matrix Model
• Phases of N=1 Supersymmetric Gauge Theories with Flavors
• Multi-Trace Superpotentials vs. Matrix Models
• Super Yang-Mills With Flavors From Large N_f Matrix Models
• Derivation of the Konishi anomaly relation from Dijkgraaf-Vafa with (Bi-)fundamental matters
• Five-Dimensional Gauge Theories and Quantum Mechanical Matrix Models
• Notes on supersymmetric Sp(N) theories with an antisymmetric tensor
• Supereigenvalue Model and Dijkgraaf-Vafa Proposal
• Exact Mesonic Vacua From Matrix Models
• Matrix-model description of N=2 gauge theories with non-hyperelliptic Seiberg-Witten curves
• Large N Strong Coupling Dynamics in Non-Supersymmetric Orbifold Field Theories
• Gravity Induced C-Deformation
• Factorization of Seiberg-Witten Curves and Compactification to Three Dimensions
• Nonperturbative Superpotentials and Compactification to Three Dimensions
• Phases and geometry of the N=1 A_2 quiver gauge theory and matrix models
• The C-Deformation of Gluino and Non-planar Diagrams
• Chern-Simons Matrix Models and Unoriented Strings
• Note on Matrix Model with Massless Flavors
• On Sp(0) factors and orientifolds
• Chiral field theories, Konishi anomalies and matrix models
• Planar Gravitational Corrections For Supersymmetric Gauge Theories
• Chiral Ring Of Sp(N) And SO(N) Supersymmetric Gauge Theory In Four Dimensions
• New Results from Glueball Superpotentials and Matrix Models: the Leigh-Strassler Deformation
• Affleck-Dine-Seiberg from Seiberg-Witten
• Mean-field Approach to the Derivation of Baryon Superpotential from Matrix Model
• Phases of N=1 USp(2N_c) Gauge Theories with Flavors
• Gravitational F-terms of N=1 Supersymmetric SU(N) Gauge Theories
• Matrix Models and Gravitational Corrections
• Phases of N=1 SO(N_c) Gauge Theories with Flavors
• The Whitham Deformation of the Dijkgraaf-Vafa Theory
• Veneziano-Yankielowicz Superpotential Terms in N=1 SUSY Gauge Theories
• Derivation of the linearity principle of Intriligator-Leigh-Seiberg
• Chiral Rings, Superpotentials and the Vacuum Structure of N=1 Supersymmetric Gauge Theories
• Note on Seiberg Duality in Matrix Model
• Towards a diagrammatic derivation of the Veneziano-Yankielowicz-Taylor superpotential
• The Glueball Superpotential
• Remarks on Phase Transitions in Matrix Models and N=1 Supersymmetric Gauge Theory
• Effective Gauge Degrees of Freedom and the (Non)existence of the Glueball Superpotential
• Notes on anomalies, baryons, and Seiberg duality
• Gaugino condensate and phases of N=1 super Yang-Mills theories
• Superpotentials for Gauge and Conformal Supergravity Backgrounds
• Les Houches lectures on supersymmetric Gauge Theories
• Matrix model, Kutasov duality and Factorization of Seiberg-Witten Curves
• Chiral rings, anomalies and loop equations in N=1* gauge theories
• The Matrix Model Curve Near the Singularities
• The Dijkgraaf-Vafa correspondence for theories with fundamental matter fields
• Glueball Superfield and Argyres Douglas Points

Cited by in corpus (44)

• Les Houches lectures on matrix models and topological strings
• Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions
• Generation of Matrix Models by W-operators
• BGWM as Second Constituent of Complex Matrix Model
• Instanton Operators and the Higgs Branch at Infinite Coupling
• Non-Abelian duality from vortex moduli: a dual model of color-confinement
• Predictions and recent results in susy on the lattice
• N=1 Superpotentials from Multi-Instanton Calculus
• Exact 2-point function in Hermitian matrix model
• Current Correlators for General Gauge Mediation
• Toric geometry and local Calabi-Yau varieties: An introduction to toric geometry (for physicists)
• Supersymmetric Gauge Theories with Flavors and Matrix Models
• Higher order loop equations for A_r and D_r quiver matrix models
• Extending the Veneziano-Yankielowicz Effective Theory
• The Holomorphic Tension of Vortices
• Deformation of Dijkgraaf-Vafa Relation via Spontaneously Broken N=2 Supersymmetry II
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• Light Nonabelian Monopoles and Generalized r-Vacua in Supersymmetric Gauge Theories
• On Nonperturbative Exactness of Konishi Anomaly and the Dijkgraaf-Vafa Conjecture
• N=1* model and glueball superpotential from Renormalization-Group-improved perturbation theory
• On the infrared behaviour of 3d Chern-Simons theories in N=2 superspace
• Deformation of Dijkgraaf-Vafa Relation via Spontaneously Broken N=2 Supersymmetry
• Improved matrix-model calculation of the N=2 prepotential
• On Confinement Index
• Chiral Rings, Anomalies and Electric-Magnetic Duality
• Effective superpotential and partial breaking of N=2 supersymmetry
• Flavour from partially resolved singularities
• Vacua of N=1 Supersymmetric QCD from Spin Chains and Matrix Models
• A note on perturbative aspects of Leigh-Strassler deformed N=4 SYM theory
• Konishi Anomalies and Curves without Adjoints
• Effective superpotential for U(N) with antisymmetric matter
• Equivalence of effective superpotentials
• The Hilbert series of 3d N=2 Yang-Mills theories with vectorlike matter
• Twisted Six Dimensional Gauge Theories on Tori, Matrix Models, and Integrable Systems
• N=1* model superpotential revisited (IR behaviour of N=4 limit)
• The Glueball Superpotential for G_2
• Effective Potentials and the Vacuum Structure of Quantum Field Theories
• Aspects of Supersymmetric Gauge Theory and String Theory
• Factorization of Seiberg-Witten Curves with Fundamental Matter
• Matrix Model and beta-deformed N=4 SYM
• Some comments on the local curve (B-side)
• Non-perturbative physics of N=1 super Yang-Mills theories
• On the Chiral Ring and Vacua of $\mathcal{N}=1$ Adjoint SQCD
• Loop Corrected Supercharges from Holomorphic Anomalies