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

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• Elliptic hypergeometry of supersymmetric dualities II. Orthogonal groups, knots, and vortices
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• Higgs branch localization of 3d N=2 theories
• Vortex partition functions, wall crossing and equivariant Gromov-Witten invariants
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• 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