The Refined Topological Vertex

Abstract

We define a refined topological vertex which depends in addition on a parameter, which physically corresponds to extending the self-dual graviphoton field strength to a more general configuration. Using this refined topological vertex we compute, using geometric engineering, a two-parameter (equivariant) instanton expansion of gauge theories which reproduce the results of Nekrasov. The refined vertex is also expected to be related to Khovanov knot invariants.

70 Pages, 23 Figures

References in corpus (2)

• Instanton counting on blowup. II. $K$-theoretic partition function
• Curves in Calabi-Yau 3-folds and Topological Quantum Field Theory

Cited by in corpus (114)

• Extended Holomorphic Anomaly in Gauge Theory
• Fiber-Base Duality and Global Symmetry Enhancement
• Exact results on ABJ theory and the refined topological string
• Surface Operator, Bubbling Calabi-Yau and AGT Relation
• Topological Strings and Quantum Spectral Problems
• Resumming the string perturbation series
• Non-supersymmetric Black Holes and Topological Strings
• Cohomological gauge theory, quiver matrix models and Donaldson-Thomas theory
• Flipping the head of T[SU(N)]: mirror symmetry, spectral duality and monopoles
• Mass-deformed $T_N$ as a linear quiver
• E + E $\to$ H
• Toric Calabi-Yau threefolds as quantum integrable systems. R-matrix and RTT relations
• Reflection states in Ding-Iohara-Miki algebra and brane-web for D-type quiver
• Operators and higher genus mirror curves
• Rank-3 antisymmetric matter on 5-brane webs
• Exact partition functions of Higgsed 5d $T_N$ theories
• Bootstrapping BPS spectra of 5d/6d field theories
• Complete prepotential for 5d $\mathcal{N}=1$ superconformal field theories
• Shifted Quiver Quantum Toroidal Algebra and Subcrystal Representations
• On AGT-W Conjecture and q-Deformed W-Algebra
• Flop Invariance of Refined Topological Vertex and Link Homologies
• Instantons from Blow-up
• Quantum geometry from the toroidal block
• On the Elliptic Genus of Three E-strings and Heterotic Strings
• Quantum toroidal algebras and solvable structures in gauge/string theory
• 5d/6d Wilson loops from blowups
• More on topological vertex formalism for 5-brane webs with O5-plane
• Direct integration for general Omega backgrounds
• Instanton counting and O-vertex
• Black Hole Entropy from Quantum Mechanics
• Localization of Vortex Partition Functions in $\mathcal{N}=(2,2)$ Super Yang-Mills theory
• Intersecting Defects and Supergroup Gauge Theory
• Supersymmetric Partition Functions and a String Theory in 4 Dimensions
• Mixed network calculus
• A Note on Instanton Effects in ABJM Theory
• Five-Brane Webs and Highest Weight Representations
• Generalized MacMahon G(q) as q-deformed CFT Correlation Function
• Symmetry enhancements via 5d instantons, qW-algebrae and (1,0) superconformal index
• The Coulomb and Higgs Branches of $\mathcal{N}=1$ Theories of Class ${\mathcal{S}}_k$
• Twisted 6d $(2,0)$ SCFTs on a Circle
• Topological vertex for 6d SCFTs with ${\mathbb{Z}}_2$-twist
• 5d AGT correspondence of supergroup gauge theories from quantum toroidal ${\mathfrak{gl}}_1$
• Entanglement entropy and edge modes in topological string theory II: The dual gauge theory story
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• Refined topological vertex with ON-planes
• Playing with the index of M-theory
• Topological strings and Wilson loops
• The spectral problem of the ABJ Fermi gas
• Motivic Donaldson-Thomas invariants of the conifold and the refined topological vertex
• Instantons and the 5D U(1) gauge theory with extra adjoint
• Thermodynamic limit of Nekrasov partition function for 5-brane web with O5-plane
• Gauge origami and quiver W-algebras
• Partition Functions and Fibering Operators on the Coulomb Branch of 5d SCFTs
• Seiberg-Witten curves with O7${}^{\pm }$-planes
• M5-branes, orientifolds, and S-duality
• Surface Operators from M-strings
• Crystal Melting, BPS Quivers and Plethystics
• Diagrammatic Expansion of Non-Perturbative Little String Free Energies
• Nekrasov's Partition Function and Refined Donaldson-Thomas Theory: the Rank One Case
• Blowup Equations for Little Strings
• Chern-Simons theory with the exceptional gauge group as a refined topological string
• Mirror of the refined topological vertex from a matrix model
• Towards Refining the Topological Strings on Compact Calabi-Yau 3-folds
• Tetrahedron instantons in Donaldson-Thomas theory
• A reduced BPS index of E-strings
• 5D N=1 super QFT: symplectic quivers
• Refined Cigar and Omega-deformed Conifold
• Evidence for an Algebra of ${\mathbf{G}}_2$ Instantons
• Geometric transition in Non-perturbative Topological string
• Dessins d'Enfants, Seiberg-Witten Curves and Conformal Blocks
• Topological String on Toric CY3s in Large Complex Structure Limit
• Instantons on Young diagrams with matters
• $DE$-type little strings from glued brane webs
• Orthosymplectic Superinstanton Counting and Brane Dynamics
• Gauge origami and quiver W-algebras III: Donaldson--Thomas $qq$-characters
• MacMahon KZ equation for Ding-Iohara-Miki algebra
• Non Planar Topological 3-Vertex Formalism
• ADHM Wilson line defect indices
• Double nested Hilbert schemes and the local stable pairs theory of curves
• The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories
• M-theory interpretation of the real topological string
• Five-dimensional gauge theories and the local B-model
• Exact Chern-Simons / Topological String duality
• Bootstrapping ADE M-strings
• Refined open topological strings revisited
• Khovanov-Rozansky cycle calculus for bipartite links
• Constant maps in equivariant topological strings and geometric modeling of fluxes
• O-vertex, O7${}^{+}$-plane, and Topological Vertex
• Refined topological amplitudes in N=1 flux compactification
• 3d $\mathcal{N}=2$ Brane Webs and Quiver Matrices
• Intersecting Surface defects and 3d Superconformal indices
• Attractor invariants, brane tilings and crystals
• Refined BPS numbers on compact Calabi-Yau threefolds from Wilson loops
• Affine characters at negative level and elliptic genera of non-critical strings
• On refined Chern-Simons / topological string duality for classical gauge groups
• Quantum $W_{1+\infty }$ subalgebras of BCD type and symmetric polynomials
• Gauge origami and quiver W-algebras IV: Pandharipande--Thomas $qq$-characters
• Recent Developments in Topological String Theory
• Generalized q-deformed Correlation Functions as Spectral Functions of Hyperbolic Geometry
• The 4-fold Pandharipande--Thomas vertex and Jeffrey--Kirwan residue
• GW/DT invariants and 5D BPS indices for strips from topological recursion
• Topological Vertex, String Amplitudes and Spectral Functions of Hyperbolic Geometry
• State counting on fibered CY-3 folds and the non-Abelian Weak Gravity Conjecture
• Aspects géométriques et intégrables des modèles de matrices aléatoires
• Singular Vector of Ding-Iohara-Miki Algebra and Hall-Littlewood Limit of 5D AGT Conjecture
• Quiver matrix model of ADHM type and BPS state counting in diverse dimensions
• More on 5d Wilson Loops in Higher-Rank Theories and Blowup Equations
• A question on generalization of partition functions of CY 3-folds in String Theory
• Free field realization of the Ding-Iohara algebra at general levels
• Direct Sum Structure of the Super Virasoro Algebra and a Fermion Algebra Arising from the Quantum Toroidal ${\mathfrak{gl}}_2$
• Topological string amplitudes and Seiberg-Witten prepotentials from the counting of dimers in transverse flux
• Intertwining operator and integrable hierarchies from topological strings
• Nonperturbative refined topological string
• Painlevé Kernels and Surface Defects at Strong Coupling