Vertices, Vortices & Interacting Surface Operators

Abstract

We show that the vortex moduli space in non-abelian supersymmetric N=(2,2) gauge theories on the two dimensional plane with adjoint and anti-fundamental matter can be described as an holomorphic submanifold of the instanton moduli space in four dimensions. The vortex partition functions for these theories are computed via equivariant localization. We show that these coincide with the field theory limit of the topological vertex on the strip with boundary conditions corresponding to column diagrams. Moreover, we resum the field theory limit of the vertex partition functions in terms of generalized hypergeometric functions formulating their AGT dual description as interacting surface operators of simple type. Analogously we resum the topological open string amplitudes in terms of q-deformed generalized hypergeometric functions proving that they satisfy appropriate finite difference equations.

22 pages, 4 figures; v.2 refs. and comments added; v.3 further comments and typos

References in corpus (54)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• N=2 dualities
• Solutions Of Four-Dimensional Field Theories Via M Theory
• Geometric Engineering of Quantum Field Theories
• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• The Topological Vertex
• Topological Strings and Integrable Hierarchies
• Vortices, Instantons and Branes
• Loop and surface operators in N=2 gauge theory and Liouville modular geometry
• Nonabelian Superconductors: Vortices and Confinement in $\mathcal{N}=2$ SQCD
• Solitons in the Higgs phase -- the moduli matrix approach --
• Vortex Strings and Four-Dimensional Gauge Dynamics
• Vortex Counting and Lagrangian 3-manifolds
• Non-Abelian String Junctions as Confined Monopoles
• Nekrasov Functions and Exact Bohr-Sommerfeld Integrals
• Disk Instantons, Mirror Symmetry and the Duality Web
• On AGT relation in the case of U(3)
• Five-dimensional AGT Conjecture and the Deformed Virasoro Algebra
• Moduli Space of Non-Abelian Vortices
• Multi-Instanton Calculus and Equivariant Cohomology
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• An Algorithm for the Microscopic Evaluation of the Coefficients of the Seiberg-Witten Prepotential
• Branes and N=2 Theories in Two Dimensions
• Correlation functions in conformal Toda field theory I
• Surface Operators in N=2 4d Gauge Theories
• Affine SL(2) conformal blocks from 4d gauge theories
• A & B model approaches to surface operators and Toda theories
• Deformed Prepotential, Quantum Integrable System and Liouville Field Theory
• Nekrasov Functions from Exact BS Periods: the Case of SU(N)
• Hitchin systems, N=2 gauge theories and W-gravity
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• Deforming SW curve
• The Power of Nekrasov Functions
• Surface Operator, Bubbling Calabi-Yau and AGT Relation
• The uses of the refined matrix model recursion
• Phase transitions, double-scaling limit, and topological strings
• On F-term contribution to effective action
• Differential equation for four-point correlation function in Liouville field theory and elliptic four-point conformal blocks
• A finite analog of the AGT relation I: finite W-algebras and quasimaps' spaces
• N=1 Superpotentials from Multi-Instanton Calculus
• Non-Perturbative Topological Strings And Conformal Blocks
• Localization with a Surface Operator, Irregular Conformal Blocks and Open Topological String
• Open topological strings and integrable hierarchies: Remodeling the A-model
• Non-abelian vortices on compact Riemann surfaces
• Generalized matrix models and AGT correspondence at all genera
• Moore-Read Fractional Quantum Hall wavefunctions and SU(2) quiver gauge theories
• Rigid Surface Operators
• Quantization of the Hitchin moduli spaces, Liouville theory, and the geometric Langlands correspondence I
• Seiberg-Witten curve via generalized matrix model
• Moduli of vortices and Grassmann manifolds
• Vortex counting from field theory
• Localization of Vortex Partition Functions in $\mathcal{N}=(2,2)$ Super Yang-Mills theory
• Quantum K-theory on flag manifolds, finite-difference Toda lattices and quantum groups
• On topological field theory representation of higher analogs of classical special functions

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• Partition functions of N=(2,2) gauge theories on S^2 and vortices
• Exact Results in D=2 Supersymmetric Gauge Theories
• Exact solution of Kerr black hole perturbations via CFT${}_2$ and instanton counting. Greybody factor, Quasinormal modes and Love numbers
• Proving AGT conjecture as HS duality: extension to five dimensions
• Non-Lagrangian Theories from Brane Junctions
• Topological strings and 5d T_N partition functions
• Surface Defects and Resolvents
• Elliptic hypergeometry of supersymmetric dualities II. Orthogonal groups, knots, and vortices
• 5D partition functions, q-Virasoro systems and integrable spin-chains
• M2-brane surface operators and gauge theory dualities in Toda
• Higgs branch localization of 3d N=2 theories
• Vortex partition functions, wall crossing and equivariant Gromov-Witten invariants
• Surface Operators and Separation of Variables
• Gauge/Liouville Triality
• Central Charges of 2d Superconformal Defects
• The Liouville side of the Vortex
• A slow review of the AGT correspondence
• Holomorphic blocks and the 5d AGT correspondence
• Intersecting Surface Defects and Two-Dimensional CFT
• Intersecting Surface Defects and Instanton Partition Functions
• Topological strings, strips and quivers
• An elliptic Virasoro symmetry in 6d
• Holomorphic Blocks for 3d Non-abelian Partition Functions
• BPS States in Omega Background and Integrability
• Quantum Hitchin Systems via beta-deformed Matrix Models
• The Stringy Instanton Partition Function
• Refined geometric transition and $qq$-characters
• A 3d-3d appetizer
• Correlation functions with fusion-channel multiplicity in W3 Toda field theory
• Modular and duality properties of surface operators in N=2* gauge theories
• 2d Partition Function in Omega-background and Vortex/Instanton Correspondence
• Intersecting Defects and Supergroup Gauge Theory
• 3d Expansions of 5d Instanton Partition Functions
• Instanton Counting, Quantum Geometry and Algebra
• Symmetry enhancements via 5d instantons, qW-algebrae and (1,0) superconformal index
• Elliptic non-Abelian Donaldson-Thomas invariants of ${\mathbb{C}}^3$
• On Integrable Structure and Geometric Transition in Supersymmetric Gauge Theories
• Orbifolds, Defects and Sphere Partition Function
• Second level semi-degenerate fields in W3 Toda theory: matrix element and differential equation
• Bootstrapping the $S^5$ partition function
• VEV of Baxter's Q-operator in N=2 gauge theory and the BPZ differential equation
• Quiver ${\text{W}}_{{\epsilon }_1,{\epsilon }_2}$ algebras of 4d $\mathcal{N}=2$ gauge theories
• AGT relation in the light asymptotic limit
• Elliptic Genus Derivation of 4d Holomorphic Blocks
• Reconstructing GKZ via topological recursion
• All Exact Solutions of Non-Abelian Vortices from Yang-Mills Instantons
• Discrete matrix models for partial sums of conformal blocks associated to Painlevé transcendents
• Towards a gauge theory interpretation of the real topological string
• Quantum mirror curve of periodic chain geometry
• $q$-Difference Kac-Schwarz Operators in Topological String Theory
• Circular quiver gauge theories, isomonodromic deformations and $W_N$ fermions on the torus
• On $q$-Isomonodromic Deformations and $q$-Nekrasov Functions
• Deformed SW curve and the null vector decoupling equation in Toda field theory