Liouville Correlation Functions from Four-dimensional Gauge Theories

Abstract

We conjecture an expression for the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures as the Nekrasov partition function of a certain class of N=2 SCFTs recently defined by one of the authors. We conduct extensive tests of the conjecture at genus 0,1.

32 pages, 8 figures; v2: minor corrections, published version

References in corpus (4)

• N=2 dualities
• The Refined Topological Vertex
• Modular bootstrap in Liouville field theory
• On Crossing Symmmetry and Modular Invariance in Conformal Field Theory and S Duality in Gauge Theory

Cited by in corpus (1027)

• Infinite Chiral Symmetry in Four Dimensions
• QCD and strongly coupled gauge theories: challenges and perspectives
• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• SUSY Gauge Theories on Squashed Three-Spheres
• Loop and surface operators in N=2 gauge theory and Liouville modular geometry
• Notes on SUSY Gauge Theories on Three-Sphere
• Partition functions of N=(2,2) gauge theories on S^2 and vortices
• Gauge Theories and Macdonald Polynomials
• Analytic Continuation of Liouville Theory
• Exact Results in D=2 Supersymmetric Gauge Theories
• Vortex Counting and Lagrangian 3-manifolds
• Nekrasov Functions and Exact Bohr-Sommerfeld Integrals
• A topologically twisted index for three-dimensional supersymmetric theories
• Entanglement Entropy at Large Central Charge
• The 4d Superconformal Index from q-deformed 2d Yang-Mills
• The Omega Deformation, Branes, Integrability, and Liouville Theory
• S-duality and 2d Topological QFT
• On AGT relation in the case of U(3)
• Five-dimensional AGT Conjecture and the Deformed Virasoro Algebra
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• On combinatorial expansion of the conformal blocks arising from AGT conjecture
• R-Twisting and 4d/2d Correspondences
• The $(2,0)$ superconformal bootstrap
• Bootstrapping the superconformal index with surface defects
• General Argyres-Douglas Theory
• Holomorphic Blocks in Three Dimensions
• Darboux coordinates, Yang-Yang functional, and gauge theory
• The Virtue of Defects in 4D Gauge Theories and 2D CFTs
• Tinkertoys for Gaiotto Duality
• M-Strings
• Supersymmetry on Curved Spaces and Holography
• W Symmetry in six dimensions
• Supersymmetric Gauge Theories on the Five-Sphere
• On the Defect Group of a 6D SCFT
• SL(2,R) Chern-Simons, Liouville, and Gauge Theory on Duality Walls
• 4d Index to 3d Index and 2d TQFT
• On non-conformal limit of the AGT relations
• BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters
• Asymptotically free N=2 theories and irregular conformal blocks
• Knot Invariants from Four-Dimensional Gauge Theory
• The $\mathcal{N}=2$ superconformal bootstrap
• Defects and Quantum Seiberg-Witten Geometry
• Exact solution of Kerr black hole perturbations via CFT${}_2$ and instanton counting. Greybody factor, Quasinormal modes and Love numbers
• Seiberg-Witten Theories on Ellipsoids
• On the Superconformal Index of Argyres-Douglas Theories
• Surface Operators in N=2 4d Gauge Theories
• The Hilbert Series of the One Instanton Moduli Space
• 5-Brane Webs, Symmetry Enhancement, and Duality in 5d Supersymmetric Gauge Theory
• Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions
• Wild Quiver Gauge Theories
• Affine SL(2) conformal blocks from 4d gauge theories
• Irregular singularities in Liouville theory
• Recursion relations in CFT and N=2 SYM theory
• Para-Liouville/Toda central charges from M5-branes
• On AGT conjecture
• Conformal blocks as Dotsenko-Fateev Integral Discriminants
• The Quiver Matrix Model and 2d-4d Conformal Connection
• A & B model approaches to surface operators and Toda theories
• The Omega deformed B-model for rigid N=2 theories
• The gravity dual of supersymmetric gauge theories on a squashed three-sphere
• Quantum Algebraic Approach to Refined Topological Vertex
• Deformed Prepotential, Quantum Integrable System and Liouville Field Theory
• Nekrasov Functions from Exact BS Periods: the Case of SU(N)
• W-symmetry, topological vertex and affine Yangian
• On Three Dimensional Quiver Gauge Theories and Integrability
• The Superconformal Index of the E_6 SCFT
• Hitchin systems, N=2 gauge theories and W-gravity
• The Volume Conjecture, Perturbative Knot Invariants, and Recursion Relations for Topological Strings
• Classical Conformal Blocks and Painleve VI
• Extended Holomorphic Anomaly in Gauge Theory
• Proving AGT conjecture as HS duality: extension to five dimensions
• Down the rabbit hole with theories of class S
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• Method of Generating q-Expansion Coefficients for Conformal Block and N=2 Nekrasov Function by beta-Deformed Matrix Model
• Five-dimensional AGT Relation and the Deformed beta-ensemble
• Non-Lagrangian Theories from Brane Junctions
• Irregular Liouville correlators and connection formulae for Heun functions
• Superpolynomials for toric knots from evolution induced by cut-and-join operators
• Resurgence and the Nekrasov-Shatashvili Limit: Connecting Weak and Strong Coupling in the Mathieu and Lam'e Systems
• Semiclassical Virasoro Blocks from AdS${}_3$ Gravity
• Instanton counting with a surface operator and the chain-saw quiver
• Exact Results for 't Hooft Loops in Gauge Theories on S^4
• How instanton combinatorics solves Painlevé VI, V and III's
• Virasoro conformal blocks in closed form
• Deforming SW curve
• Tinkertoys for the Twisted D-Series
• Ding-Iohara-Miki symmetry of network matrix models
• Exceptional Indices
• The Power of Nekrasov Functions
• Topological strings and 5d T_N partition functions
• A direct proof of AGT conjecture at beta = 1
• Gauge theories on Omega-backgrounds from non commutative Seiberg-Witten curves
• Classification of Argyres-Douglas theories from M5 branes
• Explicit examples of DIM constraints for network matrix models
• Matrix model version of AGT conjecture and generalized Selberg integrals
• M5-branes, toric diagrams and gauge theory duality
• Isomonodromic tau-functions from Liouville conformal blocks
• Two-dimensional SCFTs from D3-branes
• W-algebras as coset vertex algebras
• Super Liouville conformal blocks from N=2 SU(2) quiver gauge theories
• On the instantons and the hypermultiplet mass of N=2* super Yang-Mills on S^4
• Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT
• Perturbative partition function for a squashed S^5
• Conformal field theory of Painlevé VI
• Elliptic hypergeometry of supersymmetric dualities II. Orthogonal groups, knots, and vortices
• $t{t}^{\ast }$ equations, localization and exact chiral rings in 4d N=2 SCFTs
• Instanton moduli spaces and bases in coset conformal field theory
• Gauge Theories on ALE Space and Super Liouville Correlation Functions
• On Painlevé/gauge theory correspondence
• Seiberg-Witten theory, matrix model and AGT relation
• BPS/CFT Correspondence III: Gauge Origami partition function and qq-characters
• Fiber-Base Duality and Global Symmetry Enhancement
• N=2 supersymmetric dynamics for pedestrians
• The String Landscape, the Swampland, and the Missing Corner
• Seiberg-Witten theory as a Fermi gas
• On Combinatorial Expansions of Conformal Blocks
• Modular Invariance in Superstring Theory From $\mathcal{N}=4$ Super-Yang-Mills
• Vertex operator algebras of Argyres-Douglas theories from M5-branes
• SUSY monopole potentials in 2+1 dimensions
• Proving the AGT relation for N_f = 0,1,2 antifundamentals
• Topological Anti-Topological Fusion in Four-Dimensional Superconformal Field Theories
• Vertex Operator Algebras and 3d N=4 gauge theories
• The Resurgence of Instantons: Multi-Cut Stokes Phases and the Painleve II Equation
• Zamolodchikov asymptotic formula and instanton expansion in N=2 SUSY N_f=2N_c QCD
• A note on perturbation series in supersymmetric gauge theories
• An E7 Surprise
• Quiver W-algebras
• Hawking from Catalan
• 3d & 5d gauge theory partition functions as q-deformed CFT correlators
• Vertices, Vortices & Interacting Surface Operators
• 5D partition functions, q-Virasoro systems and integrable spin-chains
• IIB flux non-commutativity and the global structure of field theories
• Fredholm determinant and Nekrasov sum representations of isomonodromic tau functions
• Integrable structure, W-symmetry and AGT relation
• The ABCDEFG of Instantons and W-algebras
• Monodromic vs geodesic computation of Virasoro classical conformal blocks
• Proving AGT relations in the large-c limit
• M2-brane surface operators and gauge theory dualities in Toda
• Surface Operator, Bubbling Calabi-Yau and AGT Relation
• Chiral algebra of Argyres-Douglas theory from M5 brane
• Matrix models for $\beta$-ensembles from Nekrasov partition functions
• Higher-point conformal blocks and entanglement entropy in heavy states
• Holographic Aspects of Four Dimensional $\mathcal{N}=2$ SCFTs and their Marginal Deformations
• New Modular Invariants in $\mathcal{N}=4$ Super-Yang-Mills Theory
• Instantons on ALE spaces and Super Liouville Conformal Field Theories
• QNMs of branes, BHs and fuzzballs from Quantum SW geometries
• BPS/CFT correspondence IV: sigma models and defects in gauge theory
• Liouville/Toda central charges from M5-branes
• AGT on the S-duality Wall
• Direct derivation of "mirror" ABJ partition function
• Extended Supersymmetry on Curved Spaces
• On the Large $R$-charge Expansion in $\mathcal{N}=2$ Superconformal Field Theories
• The Omega Deformation From String and M-Theory
• Affine sl(N) conformal blocks from N=2 SU(N) gauge theories
• Refined BPS invariants of 6d SCFTs from anomalies and modularity
• Line operators on S^1xR^3 and quantization of the Hitchin moduli space
• Cohomological Hall algebras, vertex algebras and instantons
• Quiver Tails and N=1 SCFTs from M5-branes
• Exact results for Wilson loops in arbitrary representations
• 3-Manifolds and 3d Indices
• Twistor Approach to String Compactifications: a Review
• Sine-square deformation of solvable spin chains and conformal field theories
• Classical conformal blocks via AdS/CFT correspondence
• Topological expansion of beta-ensemble model and quantum algebraic geometry in the sectorwise approach
• CFT description of BH's and ECO's: QNMs, superradiance, echoes and tidal responses
• Line Operator Index on S1 $\times$ S3
• Quantum Geometry of Resurgent Perturbative/Nonperturbative Relations
• Supergravity one-loop corrections on AdS_7 and AdS_3, higher spins and AdS/CFT
• Instantons and 2d Superconformal field theory
• Matrix Models for Random Partitions
• Spectral Duality Between Heisenberg Chain and Gaudin Model
• 3d TQFT from 6d SCFT
• Vortex partition functions, wall crossing and equivariant Gromov-Witten invariants
• Duality Symmetric String and M-Theory
• Quantization of Integrable Systems and a 2d/4d Duality
• Tao Probing the End of the World
• On AGT Conjecture for Pure Super Yang-Mills and W-algebra
• The matrix model version of AGT conjecture and CIV-DV prepotential
• Holographic thermal correlators from supersymmetric instantons
• Deformed N=2 theories, generalized recursion relations and S-duality
• Universal correlation functions in rank 1 SCFTs
• Surface Operators and Separation of Variables
• Conformal blocks in Virasoro and W theories: duality and the Calogero-Sutherland model
• A New 2d/4d Duality via Integrability
• The uses of the refined matrix model recursion
• Non-conformal limit of AGT relation from the 1-point torus conformal block
• $(q,t)$-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces
• The Superconformal Index of Class S Theories of Type D
• N=2 gauge theories and degenerate fields of Toda theory
• Whittaker vectors of the Virasoro algebra in terms of Jack symmetric polynomial
• Towards a proof of AGT conjecture by methods of matrix models
• Quivers, YBE and 3-manifolds
• Higher-Form Symmetries, Bethe Vacua, and the 3d-3d Correspondence
• Notes on Ding-Iohara algebra and AGT conjecture
• AGT conjecture and Integrable structure of Conformal field theory for c=1
• Opers, surface defects, and Yang-Yang functional
• New Seiberg Dualities from N=2 Dualities
• Spectrum of Quantum Transfer Matrices via Classical Many-Body Systems
• Counting Exceptional Instantons
• Tinkertoys for the Z3-twisted D4 Theory
• Spiked Instantons from Intersecting D-branes
• Universal 3d Cardy Block and Black Hole Entropy
• Modular anomaly equation, heat kernel and S-duality in N=2 theories
• Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals
• Bilinear equations on Painleve tau functions from CFT
• Nekrasov prepotential with fundamental matter from the quantum spin chain
• High-Temperature Expansion of Supersymmetric Partition Functions
• The Superconformal Index of the (2,0) Theory with Defects
• Quiver Yangian and Supersymmetric Quantum Mechanics
• Exploring ${\mathcal{W}}_{\infty }$ in the quadratic basis
• Extremal Correlators and Random Matrix Theory
• 5D SYM and 2D q-Deformed YM
• Painlevé VI connection problem and monodromy of c=1 conformal blocks
• Integrability and cycles of deformed $\mathcal{N}=2$ gauge theory
• Gauge/Liouville Triality
• Isomonodromy, Painlevé Transcendents and Scattering off of Black Holes
• Cluster integrable systems, q-Painleve equations and their quantization
• Colored HOMFLY polynomials as multiple sums over paths or standard Young tableaux
• Semiclassical Analysis of the 3d/3d Relation
• Kerr-de Sitter Greybody Factors via Isomonodromy
• Virasoro vacuum block at next-to-leading order in the heavy-light limit
• Ramond sector of super Liouville theory from instantons on an ALE space
• Irregular conformal blocks and connection formulae for Painlevé V functions
• Extended Conformal Symmetry and Recursion Formulae for Nekrasov Partition Function
• Trialities of $\mathcal{W}$-algebras
• $D=6$, $\mathcal{N}=(2,0)$ and $\mathcal{N}=(4,0)$ theories
• Quantum curves for Hitchin fibrations and the Eynard-Orantin theory
• Toric Calabi-Yau threefolds as quantum integrable systems. R-matrix and RTT relations
• Chiral Liouville Gravity
• On colored HOMFLY polynomials for twist knots
• Shifted Quiver Yangians and Representations from BPS Crystals
• On "Dotsenko-Fateev" representation of the toric conformal blocks
• Classical torus conformal block, N=2* twisted superpotential and the accessory parameter of Lame equation
• Semi-classical Virasoro blocks: proof of exponentiation
• Anomaly in RTT relation for DIM algebra and network matrix models
• Central Charges of 2d Superconformal Defects
• The superconformal index and an elliptic algebra of surface defects
• From 3d dualities to 2d free field correlators and back
• Coherent states in quantum ${\mathcal{W}}_{1+\infty }$ algebra and qq-character for 5d Super Yang-Mills
• Celestial Liouville Theory for Yang-Mills Amplitudes
• Reflection states in Ding-Iohara-Miki algebra and brane-web for D-type quiver
• Check of AGT Relation for Conformal Blocks on Sphere
• Borel summability of perturbative series in 4d N=2 and 5d N=1 theories
• On Gauge Theory and Topological String in Nekrasov-Shatashvili Limit
• Mirror symmetry and line operators
• Bases in coset conformal field theory from AGT correspondence and Macdonald polynomials at the roots of unity
• The ABCDEF's of Matrix Models for Supersymmetric Chern-Simons Theories
• Emergent 3-manifolds from 4d Superconformal Indices
• Matrix models for irregular conformal blocks and Argyres-Douglas theories
• On 3d extensions of AGT relation
• Duality of subregular W-algebras and principal W-superalgebras
• Towards R-matrix construction of Khovanov-Rozansky polynomials. I. Primary $T$-deformation of HOMFLY
• Gauge Theory Wilson Loops and Conformal Toda Field Theory
• The Liouville side of the Vortex
• Two-dimensional categorified Hall algebras
• Massive Scaling Limit of beta-Deformed Matrix Model of Selberg Type
• M-theory in the Omega-background and 5-dimensional non-commutative gauge theory
• Quiver elliptic W-algebras
• Spectral dualities in XXZ spin chains and five dimensional gauge theories
• The toroidal block and the genus expansion
• From SO/Sp instantons to W-algebra blocks
• Taming Defects in $\mathcal{N}=4$ Super-Yang-Mills
• W_3 irregular states and isolated N=2 superconformal field theories
• Resolvents and Seiberg-Witten representation for Gaussian beta-ensemble
• Relaxed singular vectors, Jack symmetric functions and fractional level $\widehat{\mathfrak{sl}}(2)$ models
• F-theoretic vs microscopic description of a conformal N=2 SYM theory
• Relating Gauge Theories via Gauge/Bethe Correspondence
• Perturbative connection formulas for Heun equations
• Gauge Theories Labelled by Three-Manifolds
• Kerr-de Sitter Quasinormal Modes via Accessory Parameter Expansion
• Generalized Jack polynomials and the AGT relations for the $SU(3)$ group
• Instanton partition functions in N=2 SU(N) gauge theories with a general surface operator, and their W-algebra duals
• Decomposing Nekrasov Decomposition
• Hitchin Equation, Singularity, and N=2 Superconformal Field Theories
• RG-Whitham dynamics and complex Hamiltonian systems
• Transformations of Spherical Blocks
• Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics
• Holomorphic blocks and the 5d AGT correspondence
• A slow review of the AGT correspondence
• On spectrum of ILW hierarchy in conformal field theory
• Orbifolds and Exact Solutions of Strongly-Coupled Matrix Models
• Whittaker pairs for the Virasoro algebra and the Gaiotto - BMT states
• Intersecting Surface Defects and Two-Dimensional CFT
• Towards a 4d/2d correspondence for Sicilian quivers
• Magnetic expansion of Nekrasov theory: the SU(2) pure gauge theory
• Supersymmetric AdS3 X S2 M-theory geometries with fluxes
• Random Boundary Geometry and Gravity Dual of $T\bar{T}$ Deformation
• Wilson Loops and Chiral Correlators on Squashed Sphere
• On S-duality of the Superconformal Index on Lens Spaces and 2d TQFT
• Equations on knot polynomials and 3d/5d duality
• 2d-4d Connection between q-Virasoro/W Block at Root of Unity Limit and Instanton Partition Function on ALE Space
• Parafermionic Liouville field theory and instantons on ALE spaces
• SymTFTs and Duality Defects from 6d SCFTs on 4-manifolds
• Irregular conformal blocks, with an application to the fifth and fourth Painlevé equations
• Analysis of correlation functions in Toda theory and AGT-W relation for SU(3) quiver
• Weyl Anomalies of Four Dimensional Conformal Boundaries and Defects
• Intersecting Surface Defects and Instanton Partition Functions
• Exact WKB and abelianization for the $T_3$ equation
• Fractional quiver W-algebras
• N=2 gauge theories on toric singularities, blow-up formulae and W-algebrae
• An M-Theoretic Derivation of a 5d and 6d AGT Correspondence, and Relativistic and Elliptized Integrable Systems
• Surface defects, the superconformal index and q-deformed Yang-Mills
• Generalized Macdonald polynomials, spectral duality for conformal blocks and AGT correspondence in five dimensions
• On relation between Nekrasov functions and BS periods in pure SU(N) case
• Spectral duality in elliptic systems, six-dimensional gauge theories and topological strings
• Triality in Little String Theories
• Correlators of supersymmetric Wilson loops at weak and strong coupling
• Coset conformal blocks and N=2 gauge theories
• Twisting with a Flip (the Art of Pestunization)
• Shifted Quiver Quantum Toroidal Algebra and Subcrystal Representations
• S-duality as a beta-deformed Fourier transform
• Quarter-BPS AdS5 solutions in M-theory with a T2 bundle over a Riemann surface
• An elliptic Virasoro symmetry in 6d
• Quantization condition from exact WKB for difference equations
• Non-Perturbative Topological Strings And Conformal Blocks
• Blowup Equations for Refined Topological Strings
• AGT, Burge pairs and minimal models
• Confluent conformal blocks and the Teukolsky master equation
• Superconformal Index with Duality Domain Wall
• Holographic entanglement entropy from probe M-theory branes
• Instanton R-matrix and W-symmetry
• Exact results for perturbative partition functions of theories with SU(2|4) symmetry
• N=2 Generalized Superconformal Quiver Gauge Theory
• Holographic Description of 2D Conformal Block in Semi-classical Limit
• Exact WKB Analysis of N = 2 Gauge Theories
• Deformed Seiberg-Witten Curves for ADE Quivers
• Holography of 3d-3d correspondence at Large N
• From 6D SCFTs to Dynamic GLSMs
• Exceptional $\mathcal{N}=3$ theories
• Seiberg Duality, 5d SCFTs and Nekrasov Partition Functions
• Selberg Integral and SU(N) AGT Conjecture
• N=1 Geometries via M-theory
• Intersecting defects in gauge theory, quantum spin chains, and Knizhnik-Zamolodchikov equations
• Chiral Algebras, Localization and Surface Defects
• The large central charge limit of conformal blocks
• Quantum Holonomies from Spectral Networks and Framed BPS States
• From Brezin-Hikami to Harer-Zagier formulas for Gaussian correlators
• Painlevé representation of Tracy-Widom${}_{\beta }$ distribution for $\beta =6$
• On elementary proof of AGT relations from six dimensions
• Quantum geometry of moduli spaces of local systems and representation theory
• Non-unitary TQFTs from 3D $\mathcal{N}=4$ rank 0 SCFTs
• Liouville Conformal Field Theories in Higher Dimensions
• Classical irregular block, N=2 pure gauge theory and Mathieu equation
• Genus-one correction to asymptotically free Seiberg-Witten prepotential from Dijkgraaf-Vafa matrix model
• Riemann-Hilbert correspondence and blown up surface defects
• On genus expansion of superpolynomials
• Isomonodromic $\tau$-functions and $W_N$ conformal blocks
• N=1 theories of class S_k
• Instanton moduli spaces and $\mathcal{W}$-algebras
• Hitchin Equation, Irregular Singularity, and $N=2$ Asymptotical Free Theories
• On the timelike Liouville three-point function
• Wilson Surface Central Charge from Holographic Entanglement Entropy
• On Extensions of $\widehat{\mathfrak{gl}(m|n)}$ Kac-Moody algebras and Calabi-Yau Singularities
• Holographic duals of large-c torus conformal blocks
• BPS States in Omega Background and Integrability
• Teichmuller TQFT vs Chern-Simons Theory
• Higher laminations, webs and N=2 line operators
• M-Theoretic Derivations of 4d-2d Dualities: From a Geometric Langlands Duality for Surfaces, to the AGT Correspondence, to Integrable Systems
• Exact Quantization Conditions, Toric Calabi-Yau and Nonperturbative Topological String
• Toda Theory From Six Dimensions
• ADE Little String Theory on a Riemann Surface (and Triality)
• Torus HOMFLY as the Hall-Littlewood Polynomials
• Conformal blocks of W_N Minimal Models and AGT correspondence
• Superconformal Index and 3d-3d Correspondence for Mapping Cylinder/Torus
• Supersymmetric localization in two dimensions
• (q,t)-KZ equation for Ding-Iohara-Miki algebra
• Mayer-Cluster Expansion of Instanton Partition Functions and Thermodynamic Bethe Ansatz
• 't Hooft Operators in Gauge Theory from Toda CFT
• Classical conformal blocks from TBA for the elliptic Calogero-Moser system
• Quantum Hitchin Systems via beta-deformed Matrix Models
• Analyticity of Nekrasov Partition Functions
• Superconformal field theory and Jack superpolynomials
• On AGT description of N=2 SCFT with N_f=4
• Deformed supersymmetric gauge theories from the fluxtrap background
• Supersymmetric Gauge Theories on a Squashed Four-Sphere
• 2-parameter $\tau$-function for the first Painlevé equation -Topological recursion and direct monodromy problem via exact WKB analysis-
• Liouville reflection operator, affine Yangian and Bethe ansatz
• Infinitely many 4d $\mathcal{N}=2$ SCFTs with $a=c$ and beyond
• Generalized matrix models and AGT correspondence at all genera
• Liouville theory, N=2 gauge theories and accessory parameters
• On W-algebras and the symmetries of defects of 6d N=(2,0) theory
• A Note on Quiver Quantum Toroidal Algebra
• Introduction to localization in quantum field theory
• $q$-Virasoro/W Algebra at Root of Unity and Parafermions
• Moore-Read Fractional Quantum Hall wavefunctions and SU(2) quiver gauge theories
• Quantizing higher-spin gravity in free-field variables
• Matrix model from N = 2 orbifold partition function
• Bootstrapping 4d $\mathcal{N}=2$ gauge theories: the case of SQCD
• Splitting of surface defect partition functions and integrable systems
• SH${}^c$ Realization of Minimal Model CFT: Triality, Poset and Burge Condition
• Universal two-parameter ${\mathcal{W}}_{\infty }$-algebra and vertex algebras of type $\mathcal{W}(2,3,\dots ,N)$
• Construction of Gaiotto states with fundamental multiplets through Degenerate DAHA
• Five-dimensional SU(2) AGT conjecture and recursive formula of deformed Gaiotto state
• N=2 gauge theories and quantum phases
• Wall Crossing Invariants: from quantum mechanics to knots
• On AGT-W Conjecture and q-Deformed W-Algebra
• On determinant representation and integrability of Nekrasov functions
• Two 6d origins of 4d SCFTs: class $\mathcal{S}$ and 6d (1,0) on a torus
• Higgsed network calculus
• On 't Hooft Defects, Monopole Bubbling and Supersymmetric Quantum Mechanics
• Punctures for Theories of Class ${\mathcal{S}}_{\Gamma }$
• Crystallization of deformed Virasoro algebra, Ding-Iohara-Miki algebra and 5D AGT correspondence
• 4d Quantum Geometry from 3d Supersymmetric Gauge Theory and Holomorphic Block
• The Stringy Instanton Partition Function
• Scheme dependence of instanton counting in ALE spaces
• Exact solution for mean energy of 2d Dyson gas at beta = 1
• Feynman diagrams and $\Omega$-deformed M-theory
• S-duality as Fourier transform for arbitrary ${\epsilon }_1,{\epsilon }_2$
• Chern-Simons Theory and S-duality
• Perturbative and nonperturbative aspects of complex Chern-Simons Theory
• Complex Chern-Simons from M5-branes on the Squashed Three-Sphere
• A Rutherford-like formula for scattering off Kerr-Newman BHs and subleading corrections
• $q$-Virasoro modular double and 3d partition functions
• On the crossing relation in the presence of defects
• S-Duality and Modular Transformation as a non-perturbative deformation of the ordinary pq-duality
• N=2 Gauge Theories: Congruence Subgroups, Coset Graphs and Modular Surfaces
• R-matrix-valued Lax pairs and long-range spin chains
• Compactification on the Ω-background and the AGT correspondence
• A search for AdS5 X S2 IIB supergravity solutions dual to N = 2 SCFTs
• Classical Conformal Blocks and Accessory Parameters from Isomonodromic Deformations
• Refined geometric transition and $qq$-characters
• Gauge theories on compact toric surfaces, conformal field theories and equivariant Donaldson invariants
• W(1+infinity) algebra as a symmetry behind AGT relation
• Exact thermal correlators of holographic $CFT$s
• On the Correspondence between Surface Operators in Argyres-Douglas Theories and Modules of Chiral Algebra
• Factorization of differential expansion for antiparallel double-braid knots
• Bootstrapping closed string field theory
• Two Dimensional Renormalization Group Flows in Next to Leading Order
• Instantons from Blow-up
• Quantum Spin Systems and Supersymmetric Gauge Theories, I
• Holography of Wrapped M5-branes and Chern-Simons theory
• Heterotic Surface Defects and Dualities from 2d/4d Indices
• 3d mirror symmetry as a canonical transformation
• Ω-deformation of B-twisted gauge theories and the 3d-3d correspondence
• AGT, N-Burge partitions and W_N minimal models
• Quantization of the Hitchin moduli spaces, Liouville theory, and the geometric Langlands correspondence I
• BPS/CFT correspondence V: BPZ and KZ equations from qq-characters
• Holomorphic field realization of SH${}^c$ and quantum geometry of quiver gauge theories
• Seiberg-Witten curve via generalized matrix model
• Local logarithmic correlators as limits of Coulomb gas integrals
• From Liouville to Chern-Simons, Alternative Realization of Wilson Loop Operators in AGT Duality
• Basic hypergeometry of supersymmetric dualities
• A brief review of the 2d/4d correspondences
• Supersymmetric index on T^2 x S^2 and elliptic genus
• On 2d TQFTs whose values are holomorphic symplectic varieties
• Abstract loop equations, topological recursion, and applications
• CFT exercises for the needs of AGT
• Accessory parameters in confluent Heun equations and classical irregular conformal blocks
• β-deformed matrix model and Nekrasov partition function
• On $W$-representations of $\beta$- and $q,t$-deformed matrix models
• Quasinormal Modes of C-metric from SCFTs
• A note on the algebraic engineering of 4D $\mathcal{N}=2$ super Yang-Mills theories
• Trialities of orthosymplectic $\mathcal{W}$-algebras
• Ellipsoid partition function from Seiberg-Witten monopoles
• Surface defects in E-string compactifications and the van Diejen model
• Weakly coupled conformal manifolds in 4d
• Quantum geometry from the toroidal block
• Exact Deconstruction of the 6D (2,0) Theory
• The DOZZ Formula from the Path Integral
• On spectrum of ILW hierarchy in conformal field theory II: coset CFT's
• Abelian dualities of $\mathcal{N}=(0,4)$ boundary conditions
• Virasoro constraint for Nekrasov instanton partition function
• Elliptic beta integrals and solvable models of statistical mechanics
• New quantum toroidal algebras from 5D $\mathcal{N}=1$ instantons on orbifolds
• Notes on Enhancement of Flavor Symmetry and 5d Superconformal Index
• N=2 SUSY gauge theories on S^4
• Complete solution to Gaussian tensor model and its integrable properties
• Surface defects in gauge theory and KZ equation
• Integrable QFT and Longo-Witten endomorphisms
• Two-dimensional crystal melting and D4-D2-D0 on toric Calabi-Yau singularities
• Supersymmetric backgrounds from 5d N=1 supergravity
• More on holographic correlators: Twisted and dimensionally reduced structures
• $\mathcal{N}=2^{\ast }$ gauge theory, free fermions on the torus and Painlevé VI
• Seiberg-Witten curves and double-elliptic integrable systems
• 2D CFT blocks for the 4D class ${\mathcal{S}}_k$ theories
• Branching rules for quantum toroidal gl(n)
• Quantum toroidal algebras and solvable structures in gauge/string theory
• Correlation functions with fusion-channel multiplicity in W3 Toda field theory
• On modular transformations of non-degenerate toric conformal blocks
• Exact WKB and the quantum Seiberg-Witten curve for 4d $N=2$ pure $SU(3)$ Yang-Mills, Part I: Abelianization
• 4d F(4) gauged supergravity and black holes of class $\mathcal{F}$
• A note on the Virasoro blocks at order $1/c$
• $\mathcal{N}=1$ superconformal theories with $D_N$ blocks
• Network, Cluster coordinates and N=2 theory I
• W-algebras and surface operators in N=2 gauge theories
• Uniformization, Calogero-Moser/Heun duality and Sutherland/bubbling pants
• Large N limit of beta-ensembles and deformed Seiberg-Witten relations
• Backlund transformation of Painleve III($D_8$) tau function
• On a hyperholomorphic line bundle over the Coulomb branch
• WKB Method and Quantum Periods beyond Genus One
• Green-Schwarz Automorphisms and 6D SCFTs
• Coset conformal field theory and instanton counting on C^2/Z_p
• Parafermionic polynomials, Selberg integrals and three-point correlation function in parafermionic Liouville field theory
• Holographic Weyl Anomalies for 4d Defects in 6d SCFTs
• Classical Virasoro irregular conformal block
• S-duality and correlation functions at large R-charge
• TBA for non-perturbative moduli spaces
• Superintegrability as the hidden origin of Nekrasov calculus
• Supergroup - extended super Liouville correspondence
• Alpha- and Omega-Deformations from fluxes in M-Theory
• Large N techniques for Nekrasov partition functions and AGT conjecture
• Vertex Algebras at the Corner
• Instanton counting and O-vertex
• Maulik-Okounkov's R-matrix from Ding-Iohara-Miki algebra
• Superconformal minimal models and admissible Jack polynomials
• Quantum curves and conformal field theory
• Surface defects, flavored modular differential equations and modularity
• Bands and gaps in Nekrasov partition function
• Discrete Painleve system and the double scaling limit of the matrix model for irregular conformal block and gauge theory
• Generalized Whittaker states for instanton counting with fundamental hypermultiplets
• Direct integration for general Omega backgrounds
• Comments on knotted 1/2 BPS Wilson loops
• Monopole Bubbling via String Theory
• Lifshitz Scaling, Microstate Counting from Number Theory and Black Hole Entropy
• Quantum Cohomology and Quantum Hydrodynamics from Supersymmetric Quiver Gauge Theories
• Dimer Models, Integrable Systems and Quantum Teichmuller Space
• An $\mathcal{N}=1$ 3d-3d Correspondence
• Fiber-base duality from the algebraic perspective
• Vortex counting from field theory
• ε-Corrected Seiberg-Witten Prepotential Obtained From Half Genus Expansion in beta-Deformed Matrix Model
• Yangian associated with 2D $\mathcal{N}=1$ SCFT
• AGT/Z${}_2$
• $q$-Deformation of Corner Vertex Operator Algebras by Miura Transformation
• Triality in SU(2) Seiberg-Witten theory and Gauss hypergeometric function
• 4d partition function on S^1 x S^3 and 2d Yang-Mills with nonzero area
• Quantum periods and prepotential in $\mathcal{N}=2$ SU(2) SQCD
• Scalar/Dirac perturbations of the Reissner-Nordström black hole and Painlevé transcendents
• Refined matrix models from BPS counting
• Quantum q-Langlands Correspondence
• Modular and duality properties of surface operators in N=2* gauge theories
• A geometric recipe for twisted superpotentials
• On the six-dimensional origin of the AGT correspondence
• Argyres-Douglas theories and Liouville Irregular States
• Intersecting Defects and Supergroup Gauge Theory
• On the Jeffrey-Kirwan residue of BCD-instantons
• Illustrated study of the semi-holographic non-perturbative framework
• Elliptic Virasoro Conformal Blocks
• Dessins d'Enfants in $\mathcal{N}=2$ Generalised Quiver Theories
• The Higgs branch of Heterotic ALE instantons
• Macdonald topological vertices and brane condensates
• Lecture notes on Liouville theory and the DOZZ formula
• Confinement and Mayer cluster expansions
• Hyperbolic 3-manifolds and Cluster Algebras
• Mixed network calculus
• N=1 superconformal blocks with Ramond fields from AGT correspondence
• Coupling of two conformal field theories and Nakajima-Yoshioka blow-up equations
• Classical Virasoro irregular conformal block II
• On Monopole Bubbling Contributions to 't Hooft Loops
• Free fermions, W-algebras and isomonodromic deformations
• 3d Expansions of 5d Instanton Partition Functions
• AGT conjecture and AFLT states: a complete construction
• Supersymmetric Partition Functions and a String Theory in 4 Dimensions
• (de)Tails of Toda CFT
• Discrete Painleve system for the partition function of $N_f=2$ $SU(2)$ supersymmetric gauge theory and its double scaling limit
• Accessory parameters for Liouville theory on the torus
• Indices for 6 dimensional superconformal field theories
• From the planar limit to M-theory
• Effective gravitational couplings of four-dimensional $\mathcal{N}=2$ supersymmetric gauge theories
• Membrane Quantum Mechanics
• From Jack polynomials to minimal model spectra
• A 5d/2d/4d correspondence
• Instanton Counting, Quantum Geometry and Algebra
• On Higgs Branch Localization of Seiberg-Witten Theories on Ellipsoid
• An Elliptic Vertex of Awata-Feigin-Shiraishi type for M-strings
• Comment on integrability in Dijkgraaf-Vafa beta-ensembles
• Cauchy formula and the character ring
• Quantum spectral problems and isomonodromic deformations
• Quasi-normal modes for the D3-branes and Exact WKB analysis
• Web Construction of ABCDEFG and Affine Quiver Gauge Theories
• Exact results for boundaries and domain walls in 2d supersymmetric theories
• Perspectives of differential expansion
• The complex Liouville string: the worldsheet
• M5-brane Defect and QHE in AdS_4 x N(1,1)/N=3 SCFT
• Classical limit of irregular blocks and Mathieu functions
• S-duality, triangle groups and modular anomalies in N=2 SQCD
• Type-B Anomaly Matching and the 6D (2,0) Theory
• M5 branes and Theta Functions
• (Mis-)Matching Type-B Anomalies on the Higgs Branch
• On Factorization of Generalized Macdonald Polynomials
• Symmetry enhancements via 5d instantons, qW-algebrae and (1,0) superconformal index
• Finite ${\epsilon }_2$-corrections to the $\mathcal{N}=2$ SYM prepotential
• Spherical Hecke algebra in the Nekrasov-Shatashvili limit
• Integrability of Liouville theory: proof of the DOZZ Formula
• Logarithmic potential beta-ensembles and Feynman graphs
• The exact 8d chiral ring from 4d recursion relations
• Screening operators and Parabolic inductions for Affine W-algebras (with an appendix by Shigenori Nakatsuka)
• Gluing two affine Yangians of ${\mathfrak{gl}}_1$
• The Coulomb and Higgs Branches of $\mathcal{N}=1$ Theories of Class ${\mathcal{S}}_k$
• 't Hooft Defects and Wall Crossing in SQM
• Geometrical interpretation of the topological recursion, and integrable string theories
• Lax matrix solution of c=1 Conformal Field Theory
• Correspondences among CFTs with different W-algebra symmetry
• Non-perturbative studies of N=2 conformal quiver gauge theories
• M5-branes on S^2 x M_4: Nahm's Equations and 4d Topological Sigma-models
• Five-Brane Webs and Highest Weight Representations
• Quasimodular instanton partition function and the elliptic solution of Korteweg-de Vries equations
• Wilson Loops and Chiral Correlators on Squashed Spheres
• Elliptic recursion for 4-point superconformal blocks and bootstrap in N=1 SLFT
• Plane Partition Realization of (Web of) W-algebra Minimal Models
• Polynomials associated with fixed points on the instanton moduli space
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• Matching branches of non-perturbative conformal block at its singularity divisor
• Anyonic Defect Branes and Conformal Blocks in Twisted Equivariant Differential (TED) K-theory
• Boundary conditions in Toda theories and minimal models
• Irregular conformal block, spectral curve and flow equations
• 5d AGT correspondence of supergroup gauge theories from quantum toroidal ${\mathfrak{gl}}_1$
• On Elliptic Algebras and Large-n Supersymmetric Gauge Theories
• Baxter's T-Q equation, SU(N)/SU(2)^{N-3} correspondence and Ω-deformed Seiberg-Witten prepotential
• Quantum periods for $\mathcal{N}=2$ $SU(2)$ SQCD around the superconformal point
• A note on Wilson-'t Hooft operators
• Observations on BPS observables in 6d
• A Macdonald refined topological vertex
• Tetrahedron instantons
• Chiral SU(2)_k currents as local operators in vertex models and spin chains
• An elliptic topological vertex
• Super instanton counting and localization
• Wilson-'t Hooft lines as transfer matrices
• Challenges of beta-deformation
• $\mathcal{N}=2^{\star }$ from Topological Amplitudes in String Theory
• Parametric dependence of irregular conformal block
• Exact results in N=2 gauge theories
• N=2 gauge theories, instanton moduli spaces and geometric representation theory
• Correspondences of categories for subregular W-algebras and principal W-superalgebras
• Recursive Method for Nekrasov partition function for classical Lie groups
• Liouville's Imaginary Shadow
• Holographic Thermal Correlators for Hyperbolic $CFT$s
• Dualities in quantum integrable many-body systems and integrable probabilities -- I
• Elliptic lift of the Shiraishi function as a non-stationary double-elliptic function
• Pure N=2 Super Yang-Mills and Exact WKB
• A Note on Quiver Yangians and $\mathcal{R}$-Matrices
• Higher AGT Correspondences, W-algebras, and Higher Quantum Geometric Langlands Duality from M-Theory
• q-Painleve equation from Virasoro constraints
• Isomonodromic tau functions on a torus as Fredholm determinants, and charged partitions
• Combinatorial expressions for the tau functions of $q$-Painlevé V and III equations
• On exclusive Racah matrices $\bar{S}$ for rectangular representations
• On the large $\Omega$-deformations in the Nekrasov-Shatashvili limit of $\mathcal{N}=2^{\ast }$ SYM
• On a singular Fredholm-type integral equation arising in N=2 super Yang-Mills theories
• Super-Liouville - Double Liouville correspondence
• Elliptic modular double and 4d partition functions
• A quantum isomonodromy equation and its application to N=2 SU(N) gauge theories
• q-Vertex Operator from 5D Nekrasov Function
• $T$, $Q$ and periods in $SU(3)$ $\mathcal{N}=2$ SYM
• Beta-ensembles for toric orbifold partition function
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• Generalized Macdonald Functions on Fock Tensor Spaces and Duality Formula for Changing Preferred Direction
• On Integrable Structure and Geometric Transition in Supersymmetric Gauge Theories
• Omega-Deformed Seiberg-Witten Effective Action from the M5-brane
• Resurgence, Painleve Equations and Conformal Blocks
• Twisted holography of defect fusions
• Trinion Conformal Blocks from Topological strings
• Recursion relation for instanton counting for $SU(2)$ $\mathcal{N}=2$ SYM in NS limit of $\Omega$ background
• Bootstrapping the $S^5$ partition function
• ABCD of 't Hooft operators
• Quantum integrability from non-simply laced quiver gauge theory
• Higher rank isomonodromic deformations and W-algebras
• Coproduct for affine Yangians and parabolic induction for rectangular $W$-algebras
• Subregular W-algebras of type A
• Correspondences between WZNW models and CFTs with W-algebra symmetry
• A 4D-2D equivalence for large-N Yang-Mills theory
• Localization principle in SUSY gauge theories
• On the Integrability of Four Dimensional N=2 Gauge Theories in the Omega Background
• Generalized Rogers Ramanujan Identities from AGT Correspondence
• BPS States in the Duality Web of the Omega deformation
• N=2 superconformal blocks and instanton partition functions
• Impure Aspects of Supersymmetric Wilson Loops
• 6j symbols for the modular double, quantum hyperbolic geometry, and supersymmetric gauge theories
• Chiral observables and S-duality in N = 2* U(N) gauge theories
• Second level semi-degenerate fields in W3 Toda theory: matrix element and differential equation
• On the Renormalization Group Flow in Two Dimensional Superconformal Models
• Loop equations and topological recursion for the arbitrary-$\beta$ two-matrix model
• Localization of a supersymmetric gauge theory in the presence of a surface defect
• Gluing affine Yangians with bi-fundamentals
• Toward the Pole
• 5d gauge theories on orbifolds and 4d 't Hooft line indices
• Notes on Mayer Expansions and Matrix Models
• Exts and the AGT relations
• Exact SUSY Wilson loops on $S^3$ from $q$-Virasoro constraints
• The integral representation of solutions of KZ equation and a modification by $\mathcal{K}$ operator insertion
• On matrix-model approach to simplified Khovanov-Rozansky calculus
• N = 2 SCFTs: An M5-brane perspective
• On Quiver W-algebras and Defects from Gauge Origami
• Gauge theories on compact toric manifolds
• Lectures on nonperturbative QCD ( Nonperturbative Topological Phenomena in QCD and Related Theories)
• Off-shell structure of twisted (2,0) theory
• Integrating over quiver variety and BPS/CFT correspondence
• Modular anomaly equations and S-duality in N=2 conformal SQCD
• Tracy-Widom distribution as instanton sum of 2D IIA superstrings
• Exact conformal blocks for the W-algebras, twist fields and isomonodromic deformations
• AFLT-type Selberg integrals
• Combinatorial approach to Mathieu and Lamé equations
• VEV of Baxter's Q-operator in N=2 gauge theory and the BPZ differential equation
• Vortices on Orbifolds
• A freely generated ring for N=1 models in class S_k
• Surface Operators from M-strings
• Quiver ${\text{W}}_{{\epsilon }_1,{\epsilon }_2}$ algebras of 4d $\mathcal{N}=2$ gauge theories
• Expansions for semiclassical conformal blocks
• Exact partition functions for the $\Omega$-deformed $\mathcal{N}=2^{\ast }$ $SU(2)$ gauge theory
• The ABCDEFG of Little Strings
• ABCD of Beta Ensembles and Topological Strings
• Existence and Orthogonality of Generalized Jack Polynomials and Its $q$-Deformation
• OPE coefficients in Argyres-Douglas theories
• Gauge origami and quiver W-algebras
• Recurrence relations for the ${\mathcal{W}}_3$ conformal blocks and $\mathcal{N}=2$ SYM partition functions
• Four flavours, triality and bimodular forms
• Crystal Melting, BPS Quivers and Plethystics
• Little String Defects and Bala-Carter Theory
• Check-Operators and Quantum Spectral Curves
• Some remarks on D-branes and defects in Liouville and Toda field theories
• Residue Formulas for Prepotentials, Instanton Expansions and Conformal Blocks
• Spectral networks and Fenchel-Nielsen coordinates
• Little String Origin of Surface Defects
• AGT relation in the light asymptotic limit
• Non-integrability of the $\Omega$-deformation
• Confinement and duality in supersymmetric gauge theories
• Conformal blocks and Painlevé functions
• BPS states in the Omega-background and torus knots
• Mayer expansion of the Nekrasov pre potential: the subleading ${\epsilon }_2$-order
• On the Nekrasov Partition Function of Gauged Argyres-Douglas Theories
• On the status of DELL systems
• Norms of logarithmic primaries of Virasoro algebra
• Duality walls in the 4d N=2 SU(N) gauge theory with 2N flavours
• Tau-functions for Quiver Gauge Theories
• Whittaker vectors for $\mathcal{W}$-algebras from topological recursion
• Advances in R-matrices and their applications (after Maulik-Okounkov, Kang-Kashiwara-Kim-Oh,...)
• On Hamiltonians for Kerov functions
• Recursive Representations of Arbitrary Virasoro Conformal Blocks
• Deconstructing Little Strings with $\mathcal{N}=1$ Gauge Theories on Ellipsoids
• Condensates and instanton - torus knot duality. Hidden Physics at UV scale
• A note on S-dual basis in free fermion system
• The Holographic Dual of the $\Omega$-background
• Asymptotic M5-brane entropy from S-duality
• Twist-field representations of W-algebras, exact conformal blocks and character identities
• Argyres-Douglas Theories, S-duality and AGT Correspondence
• Super-Yang-Mills theories on S4 x R
• Polyakov relation for the sphere and higher genus surfaces
• Resumming perturbative series in the presence of monopole bubbling effects
• Gauge Invariant Computable Quantities In Timelike Liouville Theory
• Duality between Seiberg-Witten Theory and Black Hole Superradiance
• On the solution of Liouville equation
• Conformal Blocks Beyond the Semi-Classical Limit
• Double Quiver Gauge Theory and BPS/CFT Correspondence
• The Condensate from Torus Knots
• Quantum curves from refined topological recursion: the genus 0 case
• Generalized Devil's staircase and RG flows
• More on Affine Dynkin Quiver Yangians
• M2-branes and $\mathfrak{q}$-Painlevé equations
• On some 3-point functions in the $W_4$ CFT and related braiding matrix
• Partition functions of non-Lagrangian theories from the holomorphic anomaly
• Absorption cross section in gravity's rainbow from confluent Heun equation
• New Chandrasekhar transformation in Kerr spacetime
• The trouble with twisting (2,0) theory
• Mirror of the refined topological vertex from a matrix model
• Refined toric branes, surface operators and factorization of generalized Macdonald polynomials
• Seiberg-Witten Geometry of Four-Dimensional $\mathcal{N}=2$ Quiver Gauge Theories
• Chiral trace relations in $\Omega$-deformed $\mathcal{N}=2$ theories
• Conformal blocks of Chiral fields in N=2 SUSY CFT and Affine Laumon Spaces
• Kac determinant and singular vector of the level N representation of Ding-Iohara-Miki algebra
• Comments on the NSVZ $\beta$ Functions in Two-dimensional $\mathcal{N}=(0,2)$ Supersymmetric Models
• Argyres-Douglas Loci, Singularity Structures and Wall-Crossings in Pure N=2 Gauge Theories with Classical Gauge Groups
• Holomorphic Anomaly in Gauge Theory on ALE space
• Beta Deformation and Superpolynomials of (n,m) Torus Knots
• Singular modules for affine Lie algebras, and applications to irregular WZNW conformal blocks
• On solutions of the Fuji-Suzuki-Tsuda system
• A reduced BPS index of E-strings
• Virasoro blocks and quasimodular forms
• Norm of the Whittaker vector of the deformed Virasoro algebra
• Superconformal Quantum Mechanics from M2-branes
• Cluster integrable systems and spin chains
• Complex Chern-Simons theory at level k via the 3d-3d correspondence
• Pentad and triangular structures behind the Racah matrices
• On generalized Macdonald polynomials
• Seiberg-Witten equations and non-commutative spectral curves in Liouville theory
• 2D quantum gravity partition function on the fluctuating sphere
• Quiver Yangians and $\mathcal{W}$-Algebras for Generalized Conifolds
• Irregular matrix model with $\mathcal{W}$ symmetry
• Refined Cigar and Omega-deformed Conifold
• On the energy spectrum of Yang--Mills instantons over asymptotically locally flat spaces
• Comments on fusion matrix in N=1 super Liouville field theory
• Cut-and-join operators and Macdonald polynomials from the 3-Schur functions
• Faces of matrix models
• S-duality wall of SQCD from Toda braiding
• Hyperbolic deformation of the strip-equation and the accessory parameters for the torus
• Learning knot invariants across dimensions
• N=2 supersymmetric QCD and elliptic potentials
• Irregular Vertex Operators for Irregular Conformal Blocks
• OPE of Wilson-'t Hooft operators in N=4 and N=2 SYM with gauge group G=PSU(3)
• An(1) Affine Quiver Matrix Model
• Analytic properties of the Virasoro modular kernel
• Equivariant U(N) Verlinde algebra from Bethe/Gauge correspondence
• The Nested Off-shell Bethe ansatz and O(N) Matrix Difference Equations
• 6d Dual Conformal Symmetry and Minimal Volumes in AdS
• Parallel surface defects, Hecke operators, and quantum Hitchin system
• Entanglement in Theory Space
• Affine Laumon spaces and iterated W-algebras
• New results in $\mathcal{N}=2$ theories from non-perturbative string
• Two-dimensional superconformal field theories from Riemann surfaces with boundary
• Unitary matrix with a Penner-like potential also yields N_f=2
• Lectures on perverse sheaves on instanton moduli spaces
• Wall-crossing and operator ordering for 't Hooft operators in N=2 gauge theories
• Recent developments in 2d $\mathcal{N}=(2,2)$ supersymmetric gauge theories
• A Family of ${\mathrm{GL}}_r$ Multiplicative Higgs Bundles on Rational Base
• An infrared bootstrap of the Schur index with surface defects
• On Dimensional Transmutation in 1+1D Quantum Hydrodynamics
• Wilson Loop Invariants from $W_N$ Conformal Blocks
• $\widehat{\mathfrak{sl}}(n{)}_N$ WZW conformal blocks from $SU(N)$ instanton partition functions on ${\mathbb{C}}^2/{\mathbb{Z}}_n$
• Deconstructing Defects
• Penner Type Ensemble for Gauge Theories Revisited
• Dessins d'Enfants, Seiberg-Witten Curves and Conformal Blocks
• BPS dyons and Hesse flow
• Elliptic Genus Derivation of 4d Holomorphic Blocks
• Pentagon identities arising in supersymmetric gauge theory computations
• Large R-charge EFT correlators in N=2 SQCD
• Deformed Virasoro algebras from elliptic quantum algebras
• Comments on chiral algebras and $\Omega$-deformations
• On the exponentially small corrections to $\mathcal{N}=2$ superconformal correlators at large R-charge
• Irregular Singularities in the H3+ WZW Model
• Supersymmetric interactions of a six-dimensional self-dual tensor and fixed-shape second quantized strings
• Masses, Sheets and Rigid SCFTs
• Exact partition functions for deformed $\mathcal{N}=2$ theories with $N_f=4$ flavours
• Instantons on Young diagrams with matters
• Givental J-functions, Quantum integrable systems, AGT relation with surface operator
• From topological strings to minimal models
• Scattering Amplitudes and BCFW in $\mathcal{N}=2^{\ast }$ Theory
• R-matrices and Miura operators in 5d Chern-Simons theory
• Conformal field theories and compact curves in moduli spaces
• FQHE and $t{t}^{\ast }$ geometry
• On fusion kernel in Liouville theory
• On even spin $W_{\infty }$
• Quantum spectral curve for (q,t)-matrix model
• Notes on 3-point functions of A_{N-1} Toda theory and AGT-W relation for SU(N) quiver
• More Large $N$ limits of 3d gauge theories
• Twisted reduction of quiver W-algebras
• Classical Liouville Three-point Functions from Riemann-Hilbert Analysis
• Describing codimension two defects
• MacMahon KZ equation for Ding-Iohara-Miki algebra
• c-Recursion for multi-point superconformal blocks. NS sector
• More on the SW-QNM correspondence
• A strange relationship between 2d CFT and 4d gauge theory
• A new treatment for some periodic Schrödinger operators II: the wave function
• RG Domain Wall for the General su(2) Coset Models
• Fermionic fractional quantum Hall states: A modern approach to systems with bulk-edge correspondence
• Orthosymplectic Superinstanton Counting and Brane Dynamics
• Nekrasov and Argyres-Douglas theories in spherical Hecke algebra representation
• Framed sheaves on root stacks and supersymmetric gauge theories on ALE spaces
• Supersymmetric Wilson Loops, Instantons, and Deformed $\mathcal{W}$-Algebras
• Symmetries of quantum Lax equations for the Painlevé equations
• Gauge origami and quiver W-algebras III: Donaldson--Thomas $qq$-characters
• Effective Gravitational Couplings of Higher-Rank Supersymmetric Gauge Theories
• Super Topological Recursion and Gaiotto Vectors For Superconformal Blocks
• Topological AdS/CFT and the $\Omega$ deformation
• The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories
• Genus one correction to Seiberg-Witten prepotential from β-deformed matrix model
• Higher rank FZZ-dualities
• Non-stationary difference equation for q-Virasoro conformal blocks
• Wilson punctured network defects in 2D q-deformed Yang-Mills theory
• Non-Stationary Ruijsenaars Functions for $\kappa =t^{-1/N}$ and Intertwining Operators of Ding-Iohara-Miki Algebra
• Kähler Uniformization from Holographic Renormalization Group Flows of M5-branes
• Tangles, Generalized Reidemeister Moves, and Three-Dimensional Mirror Symmetry
• Four-dimensional N=2 Field Theory and Physical Mathematics
• Virasoro blocks at large exchange dimension
• Spinless basis for spin-singlet FQH states
• Quasi-Hopf twist and elliptic Nekrasov factor
• Handsaw quiver varieties and finite W-algebras
• Kerr-Newman quasinormal modes and Seiberg-Witten theory
• Partition Functions of $\mathcal{N}=1$ Gauge Theories on $S^2\times {\mathbb{R}}_{\epsilon }^2$ and Duality
• Remarks on holographic models of the Kerr-AdS${}_5$ geometry
• Cubic constraints for the resolvents of the ABJM matrix model and its cousins
• Second Order RG Flow in General su(2) Coset Models
• Seiberg-Witten period relations in Omega background
• Discrete Painleve equation, Miwa variables, and string equation in 5d matrix models
• On the Virasoro fusion and modular kernels at any irrational central charge
• The "Null-A" superintegrability for monomial matrix models
• Topological correlators of $SU(2)$, $\mathcal{N}=2^{\ast }$ SYM on four-manifolds
• Angular Momentum and Gravimagnetization of the $\mathcal{N}=2$ SYM vacuum
• Spectra of elliptic potentials and supersymmetric gauge theories
• Towards the localization of SUSY gauge theory on a curved space
• On topological field theory representation of higher analogs of classical special functions
• On new exact conformal blocks and Nekrasov functions
• F-Theory, Seiberg-Witten Curves and N = 2 Dualities
• SQCD, Superconducting Gaps and Cyclic RG Flows
• A Note on Wilson Loop in N=2 Quiver/M theory Gravity Duality
• Singular Liouville fields and spiky strings in $\rr^{1,2}$ and $SL(2,\rr)$
• Disk one-point function for non-rational conformal theories
• BPS states, crystals and matrices
• Quantum deformation of Feigin-Semikhatov's W-algebras and 5d AGT correspondence with a simple surface operator
• One-cut solution of the $\beta$-ensembles in the Zhukovsky variable
• Bootstrapping ADE M-strings
• $n$-th parafermion ${\mathcal{W}}_N$ characters from $U(N)$ instanton counting on ${\mathbb{C}}^2/{\mathbb{Z}}_n$
• Construction of 4d SYM compactified on open Riemann surfaces by the superfield formalism
• Duality Constraints on String Theory: Instantons and spectral networks
• Classical conformal blocks, Coulomb gas integrals and Richardson-Gaudin models
• Supersymmetry and the Modular Double
• Virasoro Constraint for Uglov Matrix Model
• Four-Dimensional N=2 Supersymmetric Theory with Boundary as a Two-Dimensional Complex Toda Theory
• On the structure of W-algebras in type A
• On the description of surface operators in N=2* super Yang-Mills
• Confluent Conformal Blocks of the Second Kind
• S-move matrix in the NS sector of $N=1$ super Liouville field theory
• Riemann-Hilbert treatment of Liouville theory on the torus: The general case
• Generalized Gibbs Ensemble of 2D CFTs with U(1) Charge from the AGT Correspondence
• Probabilistic conformal blocks for Liouville CFT on the torus
• Virasoro constraints revisited
• Quantum anomalies in A^{(1)}_r Toda theories with defects
• Intersecting Surface defects and 3d Superconformal indices
• Deformed planar topological open string amplitudes on Seiberg-Witten curve
• The light asymptotic limit of conformal blocks in $\mathcal{N}=1$ super Liouville field theory
• Generalized Toda Theory from Six Dimensions and the Conifold
• 4d $\mathcal{N}=1$/2d Yang-Mills Duality in Holography
• Remarks on BMS${}_3$ invariant field theories: correlation functions and nonunitary CFTs
• On 'categories' of quantum field theories
• Orbifold Vortex and Super Liouville Theory
• 4d Chern-Simons Theory as a 3d Toda Theory, and a 3d-2d Correspondence
• Super-spectral curve of irregular conformal blocks
• McKay correspondence, cohomological Hall algebras and categorification
• Painlevé equations, topological type property and reconstruction by the topological recursion
• Discrete matrix models for partial sums of conformal blocks associated to Painlevé transcendents
• On a Canonical Quantization of 3D Anti de Sitter Pure Gravity
• From Jack to Double Jack Polynomials via the Supersymmetric Bridge
• Canonical approach to the WZNW model
• Partially twisted superconformal M5 brane in R-symmetry gauge field backgrounds
• Characters, Coadjoint Orbits and Duistermaat-Heckman Integrals
• The Virasoro fusion kernel and Ruijsenaars' hypergeometric function
• Vertex Operators for Irregular Conformal Blocks: Supersymmetric Case
• The Euler anomaly and scale factors in Liouville/Toda CFTs
• Massive vector field perturbations in the Schwarzschild spacetime from supersymmetric gauge theory
• Symmetric functions in superspace: a compendium of results and open problems (including a SageMath worksheet)
• Hilbert schemes of nonreduced divisors in Calabi-Yau threefolds and W-algebras
• Circular quiver gauge theories, isomonodromic deformations and $W_N$ fermions on the torus
• Topological charges in 2d N=(2,2) theories and massive BPS states
• A-D hypersurface of $su(n)$ $\mathcal{N}=2$ supersymmetric gauge theory with $N_f=2n-2$ flavors
• Non-Perturbative Schwinger-Dyson Equations for 3d $\mathcal{N}=4$ Gauge Theories
• Non-Stationary Difference Equation and Affine Laumon Space: Quantization of Discrete Painlevé Equation
• On resummation of the irregular conformal block
• Universal consistent truncation for 6d/7d gauge/gravity duals
• Seiberg-Witten prepotential from WZNW conformal block: Langlands duality and Selberg trace formula
• The Toda system and solution to the $\mathcal{N}$=2 SUSY Yang-Mills theory
• A Surprising Relation for the Effective Coupling Constants of N=2 Super Yang-Mills Theories
• On a path integral representation of the Nekrasov instanton partition function and its Nekrasov--Shatashvili limit
• The colored Jones polynomials as vortex partition functions
• The Grassmannian VOA
• Gauge origami and quiver W-algebras IV: Pandharipande--Thomas $qq$-characters
• Construction of irregular conformal/W block and flavor mass relations of $\mathcal{N}=2$ SUSY gauge theory from the $A_{n-1}$ quiver matrix model
• Non-perturbative aspects of gauge/gravity duality
• Elliptic algebra, Frenkel-Kac construction and root of unity limit
• Large N Matrix Hyperspheres and the Gauge-Gravity Correspondence
• From $\mathcal{N}=4$ Super-Yang-Mills on ${\mathbb{RP}}^4$ to bosonic Yang-Mills on ${\mathbb{RP}}^2$
• Vector perturbations of Kerr-AdS${}_5$ and the Painlevé VI transcendent
• Interactions of Irregular Gaiotto States in Liouville Theory
• On $q$-Isomonodromic Deformations and $q$-Nekrasov Functions
• Solvable spectral problems from 2d CFT and N=2 gauge theories
• The matrix-extended $W_{1+\infty }$ algebra
• Holographic thermal correlators from recursions
• Chiral rings for surface operators in 4d and 5d SQCD
• A note on chiral trace relations from qq-characters
• Coloured refined topological vertices and parafermion conformal field theories
• Dual infrared limits of 6d $\mathcal{N}$=(2,0) theory
• AGT basis in SCFT for c=3/2 and Uglov Polynomials
• Deformed SW curve and the null vector decoupling equation in Toda field theory
• A stringy perspective on the quantum integrable model/gauge correspondence
• Schur correlation functions from q-deformed Yang-Mills
• Aspects géométriques et intégrables des modèles de matrices aléatoires
• Bethe/Gauge Correspondence for $A_N$ Spin Chains with Integrable Boundaries
• A projection formula for the ind-Grassmannian
• Diamond of triads
• Folding transformations for q-Painleve equations
• Topology of irregular isomonodromy times on a fixed pointed curve
• Non-rational su(2) cosets and Liouville field theory
• Symmetric deformed 2D/3D Hurwitz-Kontsevich model and affine Yangian of gl(1)
• Fermi-gas correlators of ADHM theory and triality symmetry
• A note on W symmetry of N=2 gauge theory
• Painlevé/CFT correspondence on a torus
• Whittaker vectors at finite energy scale, topological recursion and Hurwitz numbers
• Super-Whittaker vector at c=3/2
• BPS Z(2) monopoles and N=2 SU(n) superconformal field theories on the Higgs branch
• The thermal representation of conformal ladder integrals
• Charge functions for odd dimensional partitions
• Elliptic Quantum Toroidal Algebras, Z-algebra Structure and Representations
• Flavor deformations and supersymmetry enhancement in $4d$ $\mathcal{N}=2$ theories
• Connection formulae in the Collision Limit I: Case Studies in Lifshitz Geometry
• Conformal field theories from deformations of theories with $W_n$ symmetry
• Localization of four-dimensional super Yang-Mills theories compactified on Riemann surface
• Effective Gravitational Couplings of Kaluza-Klein Gauge Theories
• Notes on Quasinormal Modes of charged de Sitter Blackholes from Quiver Gauge Theories
• Reconstructing the boundary of AdS from an infrared defect
• Electric-magnetic Duality of Abelian Gauge Theory on the Four-torus, from the Fivebrane on T2 x T4, via their Partition Functions
• The $\mathcal{W}$-algebra bootstrap of 6d $\mathcal{N}=(2,0)$ theories
• Irregular Conformal States and Spectral Curve: Irregular Matrix Model Approach
• VEV of $Q$-operator in $U(1)$ linear quiver 5d gauge theories
• Entanglement Renyi entropy of two disjoint intervals for large $c$ Liouville field theory
• Birth of String Theory
• The light asymptotic limit of conformal blocks in Toda field theory
• Notes On U(1) Instanton Counting On $A_{l-1}$ ALE Spaces
• Bethe/Gauge correspodence: a short review on an aspect of the integrability nature of supersymmetric gauge theories
• Blowup relations on ${\mathbb{C}}^2/{\mathbb{Z}}_2$ from Nakajima-Yoshioka blowup relations
• Proof of 5D $A_n$ AGT conjecture at $\beta =1$
• Schur Connections: Chord Counting, Line Operators, and Indices
• Quasinormal Modes of Extremal Reissner-Nordstrom Black Holes via Seiberg-Witten Quantization
• The Exact Low Energy Effective action of $\mathcal{N}=2$ SYM via Seiberg-Witten Theory and Localisation
• Painlevé Kernels and Surface Defects at Strong Coupling
• Whittaker vector of deformed Virasoro algebra and Macdonald symmetric functions
• Gluing theory of Riemann surfaces and Liouville conformal field theory
• Non-Stationary Difference Equation and Affine Laumon Space II: Quantum Knizhnik-Zamolodchikov Equation
• Highest-weight vectors and three-point functions in GKO coset decomposition
• More on 5d Wilson Loops in Higher-Rank Theories and Blowup Equations
• Aspects of 4d supersymmetric dynamics and geometry
• 't Hooft surface operators in five dimensions and elliptic Ruijsenaars operators
• Spectral Problems for Quasinormal Modes of Black Holes
• Modular functors with infinite dimensional Hilbert spaces
• 5D AGT conjecture for circular quivers
• Entanglement and Excitations in Gauge/Gravity Duality
• Bosonic Higher Spin Gravity in any Dimension with Dynamical Two-Form
• Holographic thermal propagator from modularity
• Feigin-Semikhatov conjecture and related topics
• Irregular vertex algebras
• Proof of $A_n$ AGT conjecture at $\beta =1$
• Topological string amplitudes and Seiberg-Witten prepotentials from the counting of dimers in transverse flux
• Correlator correspondences for subregular $\mathcal{W}$-algebras and principal $\mathcal{W}$-superalgebras
• Free field realization of the Ding-Iohara algebra at general levels
• Classical string correspondence in $2$ and $3$ spacetime dimensions
• Functional equations of Nekrasov functions proposed by Ito-Maruyoshi-Okuda
• AGT correspondence, (q-)Painlevè equations and matrix models
• Direct Sum Structure of the Super Virasoro Algebra and a Fermion Algebra Arising from the Quantum Toroidal ${\mathfrak{gl}}_2$
• $\mathfrak{b}$-Hurwitz numbers from refined topological recursion
• Theory space of one unitary matrix model and its critical behavior associated with Argyres-Douglas theory
• Singular Vector of Ding-Iohara-Miki Algebra and Hall-Littlewood Limit of 5D AGT Conjecture
• Vertex Algebras and Commutative Algebras
• On non-stationary Lamé equation from WZW model and spin-1/2 XYZ chain