Chiral Rings and Phases of Supersymmetric Gauge Theories

Abstract

We solve for the expectation values of chiral operators in supersymmetric U(N) gauge theories with matter in the adjoint, fundamental and anti-fundamental representations. A simple geometric picture emerges involving a description by a meromorphic one-form on a Riemann surface. The equations of motion are equivalent to a condition on the integrality of periods of this form. The solution indicates that all semiclassical phases with the same number of U(1) factors are continuously connected.

55 pages

References in corpus (13)

• Chiral Rings and Anomalies in Supersymmetric Gauge Theory
• Phases of N=1 Supersymmetric Gauge Theories and Matrices
• Exact Superpotentials for Theories with Flavors via a Matrix Integral
• Matrix model approach to the N=2 U(N) gauge theory with matter in the fundamental representation
• Effective matter superpotentials from Wishart random matrices
• Adding Fundamental Matter to ``Chiral Rings and Anomalies in Supersymmetric Gauge Theory''
• Quantum moduli spaces from matrix models
• Exact superpotentials in N=1 theories with flavor and their matrix model formulation
• Perturbative Derivation of Exact Superpotential for Meson Fields from Matrix Theories with One Flavour
• Baryonic Corrections to Superpotentials from Perturbation Theory
• Adding flavor to Dijkgraaf-Vafa
• Exact Mesonic Vacua From Matrix Models
• The Phase Structure of Mass-Deformed SU(2)xSU(2) Quiver Theory

Cited by in corpus (82)

• SQCD: A Geometric Apercu
• Penner Type Matrix Model and Seiberg-Witten Theory
• Surface Defects and Resolvents
• Non-Abelian duality from vortex moduli: a dual model of color-confinement
• Quivers as Calculators: Counting, Correlators and Riemann Surfaces
• Liberating Confinement from Lagrangians: 1-form Symmetries and Lines in 4d N=1 from 6d N=(2,0)
• Multi-monopoles and Magnetic Bags
• Color superconductivity, Z_N flux tubes and monopole confinement in deformed N=2* super Yang-Mills theories
• N=1 Geometries via M-theory
• Effective Superpotentials via Konishi Anomaly
• On Unitary/Hermitian Duality in Matrix Models
• Lessons from supersymmetry: "Instead-of-Confinement" Mechanism
• Cubic curves from matrix models and generalized Konishi anomalies
• Branches of N=1 Vacua and Argyres-Douglas Points
• Supersymmetric Gauge Theories with Flavors and Matrix Models
• Non-Abelian Duality and Confinement: from N=2 to N=1 Supersymmetric QCD
• Singular points in N=2 SQCD
• Phases and geometry of the N=1 A_2 quiver gauge theory and matrix models
• Chiral field theories, Konishi anomalies and matrix models
• r Duality and "Instead-of-Confinement" Mechanism in N=1 Supersymmetric QCD
• Extending the Veneziano-Yankielowicz Effective Theory
• Critical Points of Glueball Superpotentials and Equilibria of Integrable Systems
• Special geometry of local Calabi-Yau manifolds and superpotentials from holomorphic matrix models
• The Chiral Ring and the Periods of the Resolvent
• Anomalies and phases of strongly-coupled chiral gauge theories: recent developments
• The Off-shell M5-brane and Non-Perturbative Gauge Theory
• Confining vacua in SQCD, the Konishi anomaly and the Dijkgraaf-Vafa superpotential
• Effective Field Theory Islands from Perturbative and Nonperturbative Four-Graviton Amplitudes
• The Holomorphic Tension of Nonabelian Vortices
• Light Nonabelian Monopoles and Generalized r-Vacua in Supersymmetric Gauge Theories
• Gravitational Corrections for Supersymmetric Gauge Theories with Flavors via Matrix Models
• Phases of N=1 SO(N_c) Gauge Theories with Flavors
• Exact U(N_c)-> U(N_1)xU(N_2) factorization of Seiberg-Witten curves and N=1 vacua
• Exact Superpotentials, Theories with Flavor and Confining Vacua
• On Nonperturbative Exactness of Konishi Anomaly and the Dijkgraaf-Vafa Conjecture
• Chiral Rings of Deconstructive [SU(n_c)]^N Quivers
• Nonabelian Confinement near Nontrivial Conformal Vacua
• Large N gauge theories and topological cigars
• Finiteness of Flux Vacua from Geometric Transitions
• Double Scaling Limits in Gauge Theories and Matrix Models
• The Proof of the Dijkgraaf-Vafa Conjecture and application to the mass gap and confinement problems
• Consistency conditions in the chiral ring of super Yang-Mills theories
• A Note on Domain Walls and the Parameter Space of N=1 Gauge Theories
• Confronting Seiberg's Duality with r Duality in N=1 Supersymmetric QCD
• Singularities of N=1 Supersymmetric Gauge Theory and Matrix Models
• Effective Gauge Degrees of Freedom and the (Non)existence of the Glueball Superpotential
• Superconformal R-charges and dyon multiplicities in N=2 gauge theories
• Detailing N=1 Seiberg's Duality through the Seiberg-Witten Solution of N=2
• Improved matrix-model calculation of the N=2 prepotential
• On the Geometry of Super Yang-Mills Theories: Phases and Irreducible Polynomials
• On the Geometry of Matrix Models for N=1*
• Microscopic quantum superpotential in N=1 gauge theories
• Quiver Gauge Theory and Extended Electric-magnetic Duality
• On supersymmetry breaking and the Dijkgraaf-Vafa conjecture
• The Disc Amplitude of the Dijkgraaf-Vafa Theory:1/N Expansion vs Complex Curve Analysis
• Hybrid r-Vacua in N=2 Supersymmetric QCD: Universal Condensate Formula
• Quivers via anomaly chains
• Matrix Models, Monopoles and Modified Moduli
• Duality and Modularity in Elliptic Integrable Systems and Vacua of N=1* Gauge Theories
• N=1 Duality in the Chiral Limit from N=2 Duality
• Permutations of Massive Vacua
• N=1 Super Yang-Mills Domain Walls via The Extended Veneziano Yankielowicz Theory
• G_2 Holonomy, Mirror Symmetry and Phases of N=1 SYM
• Baryon as Impurity for Phase Transition in String Landscape
• Quantum Deformation of the Effective Theory on Non-Abelian string and 2D-4D correspondence
• Remarks on the analytic structure of supersymmetric effective actions
• More on N=1 Matrix Model Curve for Arbitrary N
• The Matrix Model Curve Near the Singularities
• Chiral Rings, Futaki Invariants, Plethystics, and Groebner Bases
• Twisted Six Dimensional Gauge Theories on Tori, Matrix Models, and Integrable Systems
• Some comments about emission channels of non abelian vortices
• On effective superpotentials and Kutasov duality
• On the Chiral Ring of N=1 Supersymmetric Gauge Theories
• Singular SQCD Vacua and Confinement
• Flavors in the microscopic approach to N=1 gauge theories
• Fradkin-Shenker Continuity and "Instead-of-Confinement" Phase
• Dual Interpretations of Seiberg-Witten and Dijkgraaf-Vafa curves
• Non-perturbative physics of N=1 super Yang-Mills theories
• Matrix Model and beta-deformed N=4 SYM
• Factorization of Seiberg-Witten Curves with Fundamental Matter
• Factorized class $S$ theories and surface defects
• Unitary Matrix Model of a Chiral [SU(N)]^K Gauge Theory