The Liouville side of the Vortex

Abstract

We analyze conformal blocks with multiple (semi-)degenerate field insertions in Liouville/Toda conformal field theories an show that their vector space is fully reproduced by the four-dimensional limit of open topological string amplitudes on the strip with generic boundary conditions associated to a suitable quiver gauge theory. As a byproduct we identify the non-abelian vortex partition function with a specific fusion channel of degenerate conformal blocks.

25pages,11figures

References in corpus (11)

• Correlation functions in conformal Toda field theory I
• Para-Liouville/Toda central charges from M5-branes
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• Instanton counting with a surface operator and the chain-saw quiver
• Super Liouville conformal blocks from N=2 SU(2) quiver gauge theories
• Vertices, Vortices & Interacting Surface Operators
• Surface Operator, Bubbling Calabi-Yau and AGT Relation
• Instantons and 2d Superconformal field theory
• Seiberg-Witten prepotential from instanton counting
• Notes on Ding-Iohara algebra and AGT conjecture
• Quantum Hitchin Systems via beta-deformed Matrix Models

Cited by in corpus (34)

• Exact Results in D=2 Supersymmetric Gauge Theories
• Wild Quiver Gauge Theories
• Non-Lagrangian Theories from Brane Junctions
• Topological strings and 5d T_N partition functions
• Elliptic hypergeometry of supersymmetric dualities II. Orthogonal groups, knots, and vortices
• M2-brane surface operators and gauge theory dualities in Toda
• Vortex partition functions, wall crossing and equivariant Gromov-Witten invariants
• Surface Operators and Separation of Variables
• Central Charges of 2d Superconformal Defects
• 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
• An elliptic Virasoro symmetry in 6d
• Holomorphic Blocks for 3d Non-abelian Partition Functions
• The Stringy Instanton Partition Function
• Surface defects, flavored modular differential equations and modularity
• Modular and duality properties of surface operators in N=2* gauge theories
• Vortex counting from field theory
• 3d Expansions of 5d Instanton Partition Functions
• 2d Partition Function in Omega-background and Vortex/Instanton Correspondence
• Elliptic non-Abelian Donaldson-Thomas invariants of ${\mathbb{C}}^3$
• Exact results in N=2 gauge theories
• Orbifolds, Defects and Sphere Partition Function
• Bootstrapping the $S^5$ partition function
• Quiver ${\text{W}}_{{\epsilon }_1,{\epsilon }_2}$ algebras of 4d $\mathcal{N}=2$ gauge theories
• VEV of Baxter's Q-operator in N=2 gauge theory and the BPZ differential equation
• AGT relation in the light asymptotic limit
• Elliptic Genus Derivation of 4d Holomorphic Blocks
• All Exact Solutions of Non-Abelian Vortices from Yang-Mills Instantons
• Intersecting Surface defects and 3d Superconformal indices
• 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