On Geometry and Matrix Models

Abstract

We point out two extensions of the relation between matrix models, topological strings and N=1 supersymmetric gauge theories. First, we note that by considering double scaling limits of unitary matrix models one can obtain large N duals of the local Calabi-Yau geometries that engineer N=2 gauge theories. In particular, a double scaling limit of the Gross-Witten one-plaquette lattice model gives the SU(2) Seiberg-Witten solution, including its induced gravitational corrections. Secondly, we point out that the effective superpotential terms for N=1 ADE quiver gauge theories is similarly computed by large multi-matrix models, that have been considered in the context of ADE minimal models on random surfaces. The associated spectral curves are multiple branched covers obtained as Virasoro and W-constraints of the partition function.

24 pages

Cited by in corpus (270)

• Topological Strings and Integrable Hierarchies
• Chiral Rings and Anomalies in Supersymmetric Gauge Theory
• All genus correlation functions for the hermitian 1-matrix model
• Chern-Simons theory, matrix integrals, and perturbative three-manifold invariants
• On AGT relation in the case of U(3)
• Matrix Model as a Mirror of Chern-Simons Theory
• Hermitean matrix model free energy: Feynman graph technique for all genera
• Gravitational corrections in supersymmetric gauge theory and matrix models
• Matrix Models, Geometric Engineering and Elliptic Genera
• Free energy topological expansion for the 2-matrix model
• BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters
• Phases of N=1 Supersymmetric Gauge Theories and Matrices
• Perturbative Analysis of Gauged Matrix Models
• Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions
• SUSY Relics in One-Flavor QCD from a New 1/N Expansion
• Conformal blocks as Dotsenko-Fateev Integral Discriminants
• Supersymmetry Breaking from a Calabi-Yau Singularity
• A paradigm of open/closed duality: Liouville D-branes and the Kontsevich model
• Nekrasov Functions from Exact BS Periods: the Case of SU(N)
• Instanton counting, Macdonald function and the moduli space of D-branes
• Generation of Matrix Models by W-operators
• Holomorphic Anomaly in Gauge Theories and Matrix Models
• Matrix model version of AGT conjecture and generalized Selberg integrals
• Matrix eigenvalue model: Feynman graph technique for all genera
• M5-branes, toric diagrams and gauge theory duality
• BGWM as Second Constituent of Complex Matrix Model
• Surface Defects and Resolvents
• Resurgent Transseries and the Holomorphic Anomaly: Nonperturbative Closed Strings in Local CP2
• Chiral Rings and Phases of Supersymmetric Gauge Theories
• Saltatory de Sitter String Vacua
• S-duality of the Leigh-Strassler Deformation via Matrix Models
• The Resurgence of Instantons: Multi-Cut Stokes Phases and the Painleve II Equation
• The Dijkgraaf-Vafa prepotential in the context of general Seiberg-Witten theory
• Exact Superpotentials for Theories with Flavors via a Matrix Integral
• Non-Abelian duality from vortex moduli: a dual model of color-confinement
• Quantum parameter space and double scaling limits in N=1 super Yang-Mills theory
• Ward identities and combinatorics of rainbow tensor models
• Matrix model approach to the N=2 U(N) gauge theory with matter in the fundamental representation
• Holomorphic matrix models
• Local string models of soft supersymmetry breaking
• Quantum Geometry of Resurgent Perturbative/Nonperturbative Relations
• Unified description of correlators in non-Gaussian phases of Hermitean matrix model
• Quantization of Integrable Systems and a 2d/4d Duality
• An A_r threesome: Matrix models, 2d CFTs and 4d N=2 gauge theories
• The matrix model version of AGT conjecture and CIV-DV prepotential
• Exact Superpotentials from Matrix Models
• The Spectral Curve of the Lens Space Matrix Model
• Holomorphicity and Modularity in Seiberg-Witten Theories with Matter
• Phase Structure of a Brane/Anti-Brane System at Large N
• Partition Functions of Matrix Models as the First Special Functions of String Theory. II. Kontsevich Model
• The N=2 gauge theory prepotential and periods from a perturbative matrix model calculation
• Adding Fundamental Matter to ``Chiral Rings and Anomalies in Supersymmetric Gauge Theory''
• Unoriented Strings, Loop Equations, and N=1 Superpotentials from Matrix Models
• Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals
• Exact superpotentials in N=1 theories with flavor and their matrix model formulation
• Perturbative Computation of Glueball Superpotentials for SO(N) and USp(N)
• Brownian Motion, Chern-Simons Theory, and 2d Yang-Mills
• Konishi anomaly and N=1 effective superpotentials from matrix models
• On "Dotsenko-Fateev" representation of the toric conformal blocks
• On the Matter of the Dijkgraaf--Vafa Conjecture
• Liberating Confinement from Lagrangians: 1-form Symmetries and Lines in 4d N=1 from 6d N=(2,0)
• Massive Vacua of N=1* Theory and S-duality from Matrix Models
• Dijkgraaf-Vafa theory as large-N reduction
• (Anti)symmetric matter and superpotentials from IIB orientifolds
• Comments on Effective Superpotentials via Matrix Models
• SO(N) Superpotential, Seiberg-Witten Curves and Loop Equations
• Geometry of Spectral Curves and All Order Dispersive Integrable System
• On Low Rank Classical Groups in String Theory, Gauge Theory and Matrix Models
• Topological expansion of the 2-matrix model correlation functions: diagrammatic rules for a residue formula
• Baryons, Boundaries and Matrix Models
• Metastable Vacua, Geometrical Engineering and MQCD Transitions
• The effective action of D-branes in Calabi-Yau orientifold compactifications
• On matrix models and their $q$-deformations
• RG-Whitham dynamics and complex Hamiltonian systems
• 2D String Theory as Normal Matrix Model
• U(N) Instantons on N=1/2 superspace -- exact solution & geometry of moduli space
• Partial Breaking of N=2 Supersymmetry and of Gauge Symmetry in the U(N) Gauge Model
• Orbifolds and Exact Solutions of Strongly-Coupled Matrix Models
• Nonsupersymmetric Brane/Antibrane Configurations in Type IIA and M Theory
• Experiments with the WDVV equations for the gluino-condensate prepotential: the cubic (two-cut) case
• QCD with Chemical Potential in a Small Hyperspherical Box
• An elliptic Virasoro symmetry in 6d
• Geometric transitions and integrable systems
• Genus one contribution to free energy in hermitian two-matrix model
• W-Constraints for the Total Descendant Potential of a Simple Singularity
• Non-Perturbative Topological Strings And Conformal Blocks
• Exact 2-point function in Hermitian matrix model
• N=1 Geometries via M-theory
• A universe field theory for JT gravity
• Large N Duality, Lens Spaces and the Chern-Simons Matrix Model
• On the Coulomb Branch of a Marginal Deformation of N=4 SUSY Yang-Mills
• Adding flavor to Dijkgraaf-Vafa
• Phases of N=1 Supersymmetric Gauge Theories with Flavors
• Effective Superpotentials via Konishi Anomaly
• Massless Flavor in Geometry and Matrix Models
• Loop equations, matrix models, and N=1 supersymmetric gauge theories
• On the computation of non-perturbative effective potentials in the string theory landscape -- IIB/F-theory perspective
• Quantum parameter space in super Yang-Mills, II
• Seiberg Duality in Matrix Models II
• Non-Perturbative Quantum Geometry II
• Multi-Trace Superpotentials vs. Matrix Models
• Derivation of the Konishi anomaly relation from Dijkgraaf-Vafa with (Bi-)fundamental matters
• $\mathcal{N}=1$ Theories and a Geometric Master Field
• Super Yang-Mills With Flavors From Large N_f Matrix Models
• Matrix models with hard walls: Geometry and solutions
• Wall Crossing As Seen By Matrix Models
• Superfield theory and supermatrix model
• Metastable Vacua and Complex Deformations
• Non-perturbative effects and wall-crossing from topological strings
• Five-Dimensional Gauge Theories and Quantum Mechanical Matrix Models
• The Volume Conjecture and Topological Strings
• On Unitary/Hermitian Duality in Matrix Models
• Phases of N=1 Supersymmetric SO/Sp Gauge Theories via Matrix Model
• Branches of N=1 Vacua and Argyres-Douglas Points
• Cubic curves from matrix models and generalized Konishi anomalies
• Constructing Gauge Theory Geometries from Matrix Models
• Exact Mesonic Vacua From Matrix Models
• Effective superpotentials for B-branes in Landau-Ginzburg models
• Orientifolds, Unoriented Instantons and Localization
• Supereigenvalue Model and Dijkgraaf-Vafa Proposal
• Non-Anti-Commutative deformation of effective potentials in supersymmetric gauge theories
• Matrix-model description of N=2 gauge theories with non-hyperelliptic Seiberg-Witten curves
• Whitham Prepotential and Superpotential
• Branched Matrix Models and the Scales of Supersymmetric Gauge Theories
• An N=1 duality cascade from a deformation of N=4 SUSY Yang-Mills
• Chern-Simons matrix models, two-dimensional Yang-Mills theory and the Sutherland model
• Determination of S-curves with applications to the theory of nonhermitian orthogonal polynomials
• On the property of Cachazo-Intriligator-Vafa prepotential at the extremum of the superpotential
• Supersymmetric Gauge Theories with Flavors and Matrix Models
• Nonperturbative Superpotentials and Compactification to Three Dimensions
• Topological B-Model, Matrix Models, $\hat{c}=1$ Strings and Quiver Gauge Theories
• N=1 Gauge Theory with Flavor from Fluxes
• Quantum curves and conformal field theory
• Explicit Analysis of Kahler Deformations in 4D N=1 Supersymmetric Quiver Theories
• N=2 Quiver Gauge Model and Partial Supersymmetry Breaking
• Superintegrability as the hidden origin of Nekrasov calculus
• Higher order loop equations for A_r and D_r quiver matrix models
• Conifold geometries, topological strings and multi-matrix models
• A Novel Large-N Reduction on S^3: Demonstration in Chern-Simons Theory
• Geometrically Induced Phase Transitions at Large N
• ε-Corrected Seiberg-Witten Prepotential Obtained From Half Genus Expansion in beta-Deformed Matrix Model
• Chiral field theories from conifolds
• Note on Matrix Model with Massless Flavors
• Phases and geometry of the N=1 A_2 quiver gauge theory and matrix models
• Chern-Simons Matrix Models and Unoriented Strings
• Non-compact Topological Branes on Conifold
• Planar Gravitational Corrections For Supersymmetric Gauge Theories
• Weak coupling large-N transitions at finite baryon density
• Universal Correlators from Geometry
• The N=1* Theories on R^{1+2} X S^1 with Twisted Boundary Conditions
• Geometric Dual and Matrix Theory for $SO/Sp$ Gauge Theories
• Chiral field theories, Konishi anomalies and matrix models
• Supersymmetric SO(N)/Sp(N) Gauge Theory from Matrix Model:Exact Mesonic Vacua
• Comment on integrability in Dijkgraaf-Vafa beta-ensembles
• Critical Points of Glueball Superpotentials and Equilibria of Integrable Systems
• New Results from Glueball Superpotentials and Matrix Models: the Leigh-Strassler Deformation
• The Holomorphic Tension of Vortices
• Special geometry of local Calabi-Yau manifolds and superpotentials from holomorphic matrix models
• Generalized Yukawa couplings and Matrix Models
• The Liouville Geometry of N=2 Instantons and the Moduli of Punctured Spheres
• The Chiral Ring and the Periods of the Resolvent
• Mean-field Approach to the Derivation of Baryon Superpotential from Matrix Model
• On gauge/string correspondence and mirror symmetry
• Baxter's T-Q equation, SU(N)/SU(2)^{N-3} correspondence and Ω-deformed Seiberg-Witten prepotential
• Confining vacua in SQCD, the Konishi anomaly and the Dijkgraaf-Vafa superpotential
• The Off-shell M5-brane and Non-Perturbative Gauge Theory
• D-brane instantons and matrix models
• Extended Supersymmetric Moduli Space and a SUSY/Non-SUSY Duality
• Tensorial generalization of characters
• Irregular conformal block, spectral curve and flow equations
• Deformation of Dijkgraaf-Vafa Relation via Spontaneously Broken N=2 Supersymmetry II
• Effective Superpotentials for SO/Sp with Flavor from Matrix Models
• Phases of N=1 USp(2N_c) Gauge Theories with Flavors
• Challenges of beta-deformation
• Matrix Model Description of Baryonic Deformations
• Light Nonabelian Monopoles and Generalized r-Vacua in Supersymmetric Gauge Theories
• The Whitham Deformation of the Dijkgraaf-Vafa Theory
• Phases of N=1 SO(N_c) Gauge Theories with Flavors
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• Quantization of N=1 chiral/nonminimal (CNM) scalar multiplets and supersymmetric Yang-Mills theories
• Partial Breaking of N=2 Supersymmetry and Decoupling Limit of Nambu-Goldstone Fermion in U(N) Gauge Model
• Gravitational Corrections for Supersymmetric Gauge Theories with Flavors via Matrix Models
• Trinion Conformal Blocks from Topological strings
• Exact N=2 Supergravity Solutions With Polarized Branes
• Exact Superpotentials, Theories with Flavor and Confining Vacua
• On Nonperturbative Exactness of Konishi Anomaly and the Dijkgraaf-Vafa Conjecture
• Loop equations and topological recursion for the arbitrary-$\beta$ two-matrix model
• Veneziano-Yankielowicz Superpotential Terms in N=1 SUSY Gauge Theories
• Geometric Constructions of Two Dimensional (0,2) SUSY Theories
• Non-Critical Superstrings from Four-Dimensional Gauge Theory
• Matrix Models, Argyres-Douglas singularities and double scaling limits
• Matrix Models
• Two-Dimensional Gauge Theory and Matrix Model
• Matrix Quantum Mechanics on $S^1/{\mathbb{Z}}_2$
• Topological B-model and $\hat{c}=1$ String Theory
• Comments on Quiver Gauge Theories and Matrix Models
• Nonabelian Confinement near Nontrivial Conformal Vacua
• Chiral Rings of Deconstructive [SU(n_c)]^N Quivers
• Limit shape phase transitions: a merger of arctic circles
• A Note on Domain Walls and the Parameter Space of N=1 Gauge Theories
• The Proof of the Dijkgraaf-Vafa Conjecture and application to the mass gap and confinement problems
• Large N gauge theories and topological cigars
• Consistency conditions in the chiral ring of super Yang-Mills theories
• Off-shell M5 Brane, Perturbed Seiberg-Witten Theory, and Metastable Vacua
• Towards a diagrammatic derivation of the Veneziano-Yankielowicz-Taylor superpotential
• Check-Operators and Quantum Spectral Curves
• Double Scaling Limits in Gauge Theories and Matrix Models
• Note on Seiberg Duality in Matrix Model
• On Chebyshev Wells: Periods, Deformations, and Resurgence
• N=2 Supersymmetric SO(N)/Sp(N) Gauge Theories from Matrix Model
• Correspondence between Feynman diagrams and operators in quantum field theory that emerges from tensor model
• Deformation of Dijkgraaf-Vafa Relation via Spontaneously Broken N=2 Supersymmetry
• Singularities of N=1 Supersymmetric Gauge Theory and Matrix Models
• Determinant Formulas for Matrix Model Free Energy
• Remarks on Phase Transitions in Matrix Models and N=1 Supersymmetric Gauge Theory
• Matrix model eigenvalue integrals and twist fields in the su(2)-WZW model
• N=1* in 5 dimensions: Dijkgraaf-Vafa meets Polchinski-Strassler
• Flows between Dualities for 3d Chern-Simons Theories
• Prepotential and Instanton Corrections in N=2 Supersymmetric SU(N_1)xSU(N_2) Yang Mills Theories
• Quiver Gauge Theory and Extended Electric-magnetic Duality
• Low Energy Processes Associated with Spontaneously Broken N=2 Supersymmetry
• On supersymmetry breaking and the Dijkgraaf-Vafa conjecture
• Irregular matrix model with $\mathcal{W}$ symmetry
• The Disc Amplitude of the Dijkgraaf-Vafa Theory:1/N Expansion vs Complex Curve Analysis
• Quivers via anomaly chains
• Unitary matrix with a Penner-like potential also yields N_f=2
• Double Scaling Limits and Twisted Non-Critical Superstrings
• Improved matrix-model calculation of the N=2 prepotential
• N=1 G_2 SYM theory and Compactification to Three Dimensions
• FQHE and $t{t}^{\ast }$ geometry
• Localization on the D-brane, two-dimensional gauge theory and matrix models
• On Effective Superpotentials and Compactification to Three Dimensions
• Puzzles for Matrix Models of Chiral Field Theories
• Another Leigh-Strassler deformation through the Matrix model
• Baryon as Impurity for Phase Transition in String Landscape
• Remarks on the analytic structure of supersymmetric effective actions
• Chiral Rings, Anomalies and Electric-Magnetic Duality
• On Exact Superpotentials, Free Energies and Matrix Models
• Solving matrix models using holomorphy
• More on N=1 Matrix Model Curve for Arbitrary N
• Discrete Painleve equation, Miwa variables, and string equation in 5d matrix models
• Flavour from partially resolved singularities
• Partition functions of Supersymmetric Gauge Theories in Noncommutative R^{2D} and their Unified Perspective
• Chiral rings, anomalies and loop equations in N=1* gauge theories
• Konishi Anomalies and Curves without Adjoints
• Superpotentials, quantum parameter space and phase transitions in N=1 supersymmetric gauge theories
• The Matrix Model Curve Near the Singularities
• Planar Homological Mirror Symmetry
• On the Chiral Ring of N=1 Supersymmetric Gauge Theories
• Geometric Engineering of Seiberg-Witten Theories with Massive Hypermultiplets
• SUSY/Non-SUSY Duality in U(N) Gauge Model with Partially Broken N=2 Supersymmetry
• Spectral curves in gauge/string dualities: integrability, singular sectors and regularization
• Twisted Six Dimensional Gauge Theories on Tori, Matrix Models, and Integrable Systems
• Quantum Geometries of $A_2$
• Strong Coupling Limit of A Family of Chern-Simons-matter Theories
• Phases in WLZZ Matrix Models
• Remarks on the eigenvalues distributions of D\leq 4 Yang-Mills matrix models
• Irregular Conformal States and Spectral Curve: Irregular Matrix Model Approach
• Dual Interpretations of Seiberg-Witten and Dijkgraaf-Vafa curves
• On {\cal N}=1 exact superpotentials from U(N) matrix models
• Geometric Metastability, Quivers and Holography
• Topological B-Model and \hat{c}=1 Fermionic Strings
• Konishi Anomalies and N=1 Curves
• Unitary Matrix Model of a Chiral [SU(N)]^K Gauge Theory
• A Nonperturbative Proof of Dijkgraaf-Vafa Conjecture
• Factorized class $S$ theories and surface defects
• Quantum chaos in 2D gravity
• The universality class of the first levels in low-dimensional gravity
• Effective SO Superpotential for N=1 Theory with N_f Fundamental Matter
• On the Multi Trace Superpotential and Corresponding Matrix Model