A slow review of the AGT correspondence

Abstract

Starting with a gentle approach to the AGT correspondence from its 6d origin, these notes provide a wide (albeit shallow) survey of the literature on numerous extensions of the correspondence up to early 2020. This is an extended writeup of the lectures given at the Winter School YRISW 2020, to appear in a special issue of JPhysA. Class S is a wide class of 4d $N=2$ supersymmetric gauge theories (ranging from super-QCD to non-Lagrangian theories) obtained by twisted compactification of 6d $N=(2,0)$ superconformal theories on a Riemann surface. This 6d construction yields the Coulomb branch and Seiberg-Witten geometry of class S theories, geometrizes S-duality, and leads to the AGT correspondence, which states that many observables of class S theories are equal to 2d CFT correlators. For instance, the four-sphere partition function of a 4d $N=2$ SU(2) superconformal quiver theory is equal to a Liouville CFT correlator of primary operators. Extensions of the AGT correspondence abound: asymptotically-free gauge theories and Argyres-Douglas theories correspond to irregular CFT operators, quivers with higher-rank gauge groups and non-Lagrangian tinkertoys such as $T_N$ correspond to Toda CFT correlators, and nonlocal operators (Wilson-'t Hooft loops, surface operators, domain walls) correspond to Verlinde networks, degenerate primary operators, braiding and fusion kernels, and Riemann surfaces with boundaries.

arXiv comment106 pages plus 1309 refs. Published version

References in corpus (1007)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Liouville Correlation Functions from Four-dimensional Gauge Theories
• N=2 dualities
• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• Solutions Of Four-Dimensional Field Theories Via M Theory
• Structure Constants and Conformal Bootstrap in Liouville Field Theory
• S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory
• A Strong Coupling Test of S-Duality
• Supersymmetric Yang-Mills Systems And Integrable Systems
• Solving the 3D Ising Model with the Conformal Bootstrap
• Small Instantons in String Theory
• Geometric Engineering of Quantum Field Theories
• W-symmetry in Conformal Field Theory
• New Phenomena in SU(3) Supersymmetric Gauge Theory
• Infinite Chiral Symmetry in Four Dimensions
• Open P-Branes
• Matrix Models, Topological Strings, and Supersymmetric Gauge Theories
• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Reading between the lines of four-dimensional gauge theories
• The Topological Vertex
• Rigid Supersymmetric Theories in Curved Superspace
• New N=2 Superconformal Field Theories in Four Dimensions
• SUSY Gauge Theories on Squashed Three-Spheres
• Integrability and Seiberg-Witten Exact Solution
• Four-dimensional wall-crossing via three-dimensional field theory
• Two and three-point functions in Liouville theory
• The Refined Topological Vertex
• Loop and surface operators in N=2 gauge theory and Liouville modular geometry
• Janus Configurations, Chern-Simons Couplings, And The Theta-Angle in N=4 Super Yang-Mills Theory
• A Perturbative Window into Non-Perturbative Physics
• Notes on SUSY Gauge Theories on Three-Sphere
• Two-Dimensional Black Hole and Singularities of CY Manifolds
• Supersymmetric vacua and Bethe ansatz
• Liouville theory revisited
• Self-Dual Strings and N=2 Supersymmetric Field Theory
• Integrating Over Higgs Branches
• The Moduli Space of N=2 SUSY QCD and Duality in N=1 SUSY QCD
• Wall-crossing, Hitchin Systems, and the WKB Approximation
• Integrable systems and supersymmetric gauge theory
• Partition functions of N=(2,2) gauge theories on S^2 and vortices
• Gauge Theories and Macdonald Polynomials
• Wilson-'t Hooft operators in four-dimensional gauge theories and S-duality
• Exact half-BPS Type IIB interface solutions I: Local solution and supersymmetric Janus
• Localization techniques in quantum field theories
• 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
• An N=2 Superconformal Fixed Point with E_6 Global Symmetry
• Atomic Classification of 6D SCFTs
• S-duality in N=2 supersymmetric gauge theories
• A Dilatonic Deformation of AdS_5 and its Field Theory Dual
• Webs of five-branes and N=2 superconformal field theories
• Quantum integrability and supersymmetric vacua
• The 4d Superconformal Index from q-deformed 2d Yang-Mills
• The Omega Deformation, Branes, Integrability, and Liouville Theory
• Clebsch-Gordan and Racah-Wigner coefficients for a continuous series of representations of U_q(sl(2,R))
• Superconformal Fixed Points with E_n Global Symmetry
• S-duality and 2d Topological QFT
• Four-Dimensional SCFTs from M5-Branes
• A brief review of "little string theories"
• 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
• Nilpotent orbits and codimension-two defects of 6d N=(2,0) theories
• R-Twisting and 4d/2d Correspondences
• Mirrors of 3d Sicilian theories
• Black and super p-branes in diverse dimensions
• Bootstrapping the superconformal index with surface defects
• General Argyres-Douglas Theory
• Issues in Topological Gauge 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
• Quantum Affine Algebras and Deformations of the Virasoro and W-algebras
• A Quantum Deformation of the Virasoro Algebra and the Macdonald Symmetric Functions
• Tinkertoys for Gaiotto Duality
• Quantum Groups and Quantum Cohomology
• Spectral networks
• Schur Indices, BPS Particles, and Argyres-Douglas Theories
• Matrix Models, Geometric Engineering and Elliptic Genera
• W Symmetry in six dimensions
• Witten Index and Wall Crossing
• Gauge Theory Loop Operators and Liouville Theory
• 2d Index and Surface operators
• Exploring Curved Superspace
• Sicilian gauge theories and N=1 dualities
• Supersymmetric Gauge Theories on the Five-Sphere
• Exactly Marginal Deformations and Global Symmetries
• On the Defect Group of a 6D SCFT
• SL(2,R) Chern-Simons, Liouville, and Gauge Theory on Duality Walls
• Liouville bootstrap via harmonic analysis on a noncompact quantum group
• Refined BPS state counting from Nekrasov's formula and Macdonald functions
• Quantum W-algebras and Elliptic Algebras
• 4d Index to 3d Index and 2d TQFT
• Correlation Functions of Coulomb Branch Operators
• Integrability and Seiberg-Witten Theory: Curves and Periods
• On non-conformal limit of the AGT relations
• ABCD of instantons
• Quantum $W_N$ Algebras and Macdonald Polynomials
• N=1 Deformations and RG Flows of N=2 SCFTs
• BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters
• The dual of Janus -:- an interface CFT
• Direct Integration of the Topological String
• Knot Invariants from Four-Dimensional Gauge Theory
• Factorisation of N = 2 theories on the squashed 3-sphere
• The $\mathcal{N}=2$ superconformal bootstrap
• Enhancement of Supersymmetry via Renormalization Group Flow and the Superconformal Index
• Correlation functions in conformal Toda field theory I
• Wall-Crossing in Coupled 2d-4d Systems
• Defects and Quantum Seiberg-Witten Geometry
• Seiberg-Witten Theories on Ellipsoids
• Surface Operators in N=2 4d Gauge Theories
• On the Superconformal Index of Argyres-Douglas Theories
• A lecture on the Liouville vertex operators
• The Hilbert Series of the One Instanton Moduli Space
• Sigma Models And The ADHM Construction Of Instantons
• Wild Quiver Gauge Theories
• Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions
• Affine SL(2) conformal blocks from 4d gauge theories
• Irregular singularities in Liouville theory
• Small Instantons, Little Strings and Free Fermions
• Tinkertoys for the D_N series
• The affine Yangian of ${\mathfrak{gl}}_1$ revisited
• 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
• Fivebranes and 3-manifold homology
• Interface Yang-Mills, Supersymmetry, and Janus
• The elliptic Hall algebra and the equivariant K-theory of the Hilbert scheme of ${\mathbb{A}}^2$
• The Omega deformed B-model for rigid N=2 theories
• The Relation between Quantum W algebras and Lie algebras
• Walls, Lines, and Spectral Dualities in 3d Gauge Theories
• Recursive representation of the torus 1-point conformal block
• The gravity dual of supersymmetric gauge theories on a squashed three-sphere
• Quantum Algebraic Approach to Refined Topological Vertex
• Super Janus
• Deformed Prepotential, Quantum Integrable System and Liouville Field Theory
• Correlation functions in conformal Toda field theory II
• Nekrasov Functions from Exact BS Periods: the Case of SU(N)
• N=1 Deformations and RG Flows of N=2 SCFTs, Part II: Non-principal deformations
• On Three Dimensional Quiver Gauge Theories and Integrability
• 6D SCFTs and Phases of 5D Theories
• W-symmetry, topological vertex and affine Yangian
• The Superconformal Index of the E_6 SCFT
• Hitchin systems, N=2 gauge theories and W-gravity
• Chiral algebras of class S
• Six-dimensional D_N theory and four-dimensional SO-USp quivers
• The Volume Conjecture, Perturbative Knot Invariants, and Recursion Relations for Topological Strings
• Classical Conformal Blocks and Painleve VI
• Proving AGT conjecture as HS duality: extension to five dimensions
• Extended Holomorphic Anomaly in Gauge Theory
• BPS Bounds for Worldvolume Branes
• Matone's Relation in the Presence of Gravitational Couplings
• Method of Generating q-Expansion Coefficients for Conformal Block and N=2 Nekrasov Function by beta-Deformed Matrix Model
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• Five-dimensional AGT Relation and the Deformed beta-ensemble
• Non-Lagrangian Theories from Brane Junctions
• Instanton counting, Macdonald function and the moduli space of D-branes
• Topological Strings and Nekrasov's formulas
• On the Hall algebra of an elliptic curve, I
• Top Down Approach to 6D SCFTs
• 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
• (0,2) Trialities
• Exact Results for 't Hooft Loops in Gauge Theories on S^4
• More on the N=2 superconformal systems of type $D_p(G)$
• Lagrangians for generalized Argyres-Douglas theories
• Coulomb Branch and The Moduli Space of Instantons
• How instanton combinatorics solves Painlevé VI, V and III's
• Schur duality in the toroidal setting
• Virasoro conformal blocks in closed form
• Tinkertoys for the Twisted D-Series
• Deforming SW curve
• Ding-Iohara-Miki symmetry of network matrix models
• Gauge theories on Omega-backgrounds from non commutative Seiberg-Witten curves
• Classification of Argyres-Douglas theories from M5 branes
• Exceptional Indices
• A direct proof of AGT conjecture at beta = 1
• The Power of Nekrasov Functions
• Topological strings and 5d T_N partition functions
• Heisenberg action in the equivariant K-theory of Hilbert schemes via Shuffle Algebra
• Matrix model version of AGT conjecture and generalized Selberg integrals
• Explicit examples of DIM constraints for network matrix models
• Penner Type Matrix Model and Seiberg-Witten Theory
• Isomonodromic tau-functions from Liouville conformal blocks
• Deformation quantization and superconformal symmetry in three dimensions
• M5-branes, toric diagrams and gauge theory duality
• Two-dimensional SCFTs from D3-branes
• Stress-tensor OPE in N=2 Superconformal Theories
• Surface Defects and Chiral Algebras
• Super Liouville conformal blocks from N=2 SU(2) quiver gauge theories
• Surface Defects and Resolvents
• 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
• The superconformal index of N=1 class S fixed points
• Quantum continuous ${\mathfrak{gl}}_{\infty }$: Semi-infinite construction of representations
• BPS/CFT correspondence II: Instantons at crossroads, Moduli and Compactness Theorem
• Conformal field theory of Painlevé VI
• On the 6d origin of discrete additional data of 4d gauge theories
• Infrared Computations of Defect Schur Indices
• $t{t}^{\ast }$ equations, localization and exact chiral rings in 4d N=2 SCFTs
• Infinitely many N=2 SCFT with ADE flavor symmetry
• Instanton moduli spaces and bases in coset conformal field theory
• Gauge Theories on ALE Space and Super Liouville Correlation Functions
• Loop operators and S-duality from curves on Riemann surfaces
• Seiberg-Witten theory, matrix model and AGT relation
• On Painlevé/gauge theory correspondence
• N=2 supersymmetric dynamics for pedestrians
• BPS/CFT Correspondence III: Gauge Origami partition function and qq-characters
• Braids, Walls, and Mirrors
• Universal RG Flows Across Dimensions and Holography
• Bootstrapping $\mathcal{N}=3$ superconformal theories
• On Combinatorial Expansions of Conformal Blocks
• A note on instanton counting for N=2 gauge theories with classical gauge groups
• 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
• AdS/CFT Dual Pairs from M5-Branes on Riemann Surfaces
• Vertex Operator Algebras and 3d N=4 gauge theories
• Topological Anti-Topological Fusion in Four-Dimensional Superconformal Field Theories
• A "Lagrangian" for a non-Lagrangian theory
• A note on perturbation series in supersymmetric gauge theories
• New N=1 Dualities
• Zamolodchikov asymptotic formula and instanton expansion in N=2 SUSY N_f=2N_c QCD
• The Resurgence of Instantons: Multi-Cut Stokes Phases and the Painleve II Equation
• Hawking from Catalan
• More $\mathcal{N}=4$ superconformal bootstrap
• Quiver W-algebras
• 3d Chern-Simons Theory from M5-branes
• 3d & 5d gauge theory partition functions as q-deformed CFT correlators
• Vertices, Vortices & Interacting Surface Operators
• IIB flux non-commutativity and the global structure of field theories
• E-String Theory on Riemann Surfaces
• 5D partition functions, q-Virasoro systems and integrable spin-chains
• Monodromic vs geodesic computation of Virasoro classical conformal blocks
• Fredholm determinant and Nekrasov sum representations of isomonodromic tau functions
• Central charges and RG flow of strongly-coupled N=2 theory
• Proving AGT relations in the large-c limit
• M2-brane surface operators and gauge theory dualities in Toda
• Coulomb Branch Operators and Mirror Symmetry in Three Dimensions
• Integrable structure, W-symmetry and AGT relation
• The ABCDEFG of Instantons and W-algebras
• Surface Operator, Bubbling Calabi-Yau and AGT Relation
• Chiral algebra of Argyres-Douglas theory from M5 brane
• Higher-point conformal blocks and entanglement entropy in heavy states
• Matrix models for $\beta$-ensembles from Nekrasov partition functions
• Holographic Aspects of Four Dimensional $\mathcal{N}=2$ SCFTs and their Marginal Deformations
• N=1 Lagrangians for generalized Argyres-Douglas theories
• From the Weyl Anomaly to Entropy of Two-Dimensional Boundaries and Defects
• Chiral Algebras for Trinion Theories
• A limit for large $R$-charge correlators in $\mathcal{N}=2$ theories
• 4d $\mathcal{N}$=2 theories with disconnected gauge groups
• Instantons on ALE spaces and Super Liouville Conformal Field Theories
• Extended Supersymmetry on Curved Spaces
• VOAs labelled by complex reflection groups and 4d SCFTs
• AGT on the S-duality Wall
• BPS/CFT correspondence IV: sigma models and defects in gauge theory
• Liouville/Toda central charges from M5-branes
• On the Large $R$-charge Expansion in $\mathcal{N}=2$ Superconformal Field Theories
• 5d Partition Functions with A Twist
• D-type Conformal Matter and SU/USp Quivers
• Factorisation and holomorphic blocks in 4d
• The Omega Deformation From String and M-Theory
• 5-brane webs for 5d $\mathcal{N}=1$ $G_2$ gauge theories
• 3d Modularity
• The elliptic Hall algebra, Cherednick Hecke algebras and Macdonald polynomials
• Affine sl(N) conformal blocks from N=2 SU(N) gauge theories
• Quiver Tails and N=1 SCFTs from M5-branes
• Universal Features of BPS Strings in Six-dimensional SCFTs
• Cohomological Hall algebras, vertex algebras and instantons
• Argyres-Seiberg duality and the Higgs branch
• Line operators on S^1xR^3 and quantization of the Hitchin moduli space
• On 4d rank-one N=3 superconformal field theories
• Exact results for Wilson loops in arbitrary representations
• Twistor Approach to String Compactifications: a Review
• Exploring Curved Superspace (II)
• Classification of 4d N=2 gauge theories
• Compactification of 6d minimal SCFTs on Riemann surfaces
• Classical conformal blocks via AdS/CFT correspondence
• Supergravity one-loop corrections on AdS_7 and AdS_3, higher spins and AdS/CFT
• The supersymmetric index in four dimensions
• Line Operator Index on S1 $\times$ S3
• Matrix Models for Random Partitions
• Instantons and 2d Superconformal field theory
• Argyres-Douglas Theories, the Macdonald Index, and an RG Inequality
• Spectral Duality Between Heisenberg Chain and Gaudin Model
• $(0,4)$ dualities
• 3d TQFT from 6d SCFT
• Spectral Duality in Integrable Systems from AGT Conjecture
• Correlators of the symmetric product orbifold
• Operator Mixing in Large $N$ Superconformal Field Theories on ${\mathbb{S}}^4$ and Correlators with Wilson loops
• (p,q)-webs of DIM representations, 5d N=1 instanton partition functions and qq-characters
• Quantization of Integrable Systems and a 2d/4d Duality
• Hilbert Series for Moduli Spaces of Two Instantons
• Global Properties of Supersymmetric Theories and the Lens Space
• An A_r threesome: Matrix models, 2d CFTs and 4d N=2 gauge theories
• Finalizing the proof of AGT relations with the help of the generalized Jack polynomials
• Compactifications of 6d $N=(1,0)$ SCFTs with non-trivial Stiefel-Whitney classes
• Codimension-two defects and Argyres-Douglas theories from outer-automorphism twist in 6d $(2,0)$ theories
• Deformed N=2 theories, generalized recursion relations and S-duality
• On AGT Conjecture for Pure Super Yang-Mills and W-algebra
• Universal correlation functions in rank 1 SCFTs
• The matrix model version of AGT conjecture and CIV-DV prepotential
• tt* Geometry in 3 and 4 Dimensions
• Conformal blocks in Virasoro and W theories: duality and the Calogero-Sutherland model
• Line defects and 5d instanton partition functions
• Superconformal surfaces in four dimensions
• Surface Operators and Separation of Variables
• Large N Correlation Functions in Superconformal Field Theories
• Compactifications of ADE conformal matter on a torus
• A New 2d/4d Duality via Integrability
• M5 brane and four dimensional N=1 theories I
• Conformal Manifolds in Four Dimensions and Chiral Algebras
• Non-conformal limit of AGT relation from the 1-point torus conformal block
• 5d/6d DE instantons from trivalent gluing of web diagrams
• Argyres-Douglas Theories, S^1 Reductions, and Topological Symmetries
• The uses of the refined matrix model recursion
• $(q,t)$-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces
• N=2 gauge theories and degenerate fields of Toda theory
• Whittaker vectors of the Virasoro algebra in terms of Jack symmetric polynomial
• M2-branes and AdS/CFT
• The Superconformal Index of Class S Theories of Type D
• $\mathcal{N}=2$ central charge bounds from $2d$ chiral algebras
• Categorical Tinkertoys for N=2 Gauge Theories
• Universal Spinning Black Holes and Theories of Class $\mathcal{R}$
• Argyres-Douglas Theories, Chiral Algebras and Wild Hitchin Characters
• The algebra of Wilson-'t Hooft operators
• Three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories and partition functions on Seifert manifolds: A review
• 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
• AGT conjecture and Integrable structure of Conformal field theory for c=1
• Notes on Ding-Iohara algebra and AGT conjecture
• Mass-deformed $T_N$ as a linear quiver
• Comments on scaling limits of 4d N=2 theories
• Opers, surface defects, and Yang-Yang functional
• Spiked Instantons from Intersecting D-branes
• Large-N correlation functions in $\mathcal{N}=2$ superconformal QCD
• Spectrum of Quantum Transfer Matrices via Classical Many-Body Systems
• Four-dimensional Quantum Gravity with a Cosmological Constant from Three-dimensional Holomorphic Blocks
• Counting Exceptional Instantons
• On Irregular Singularity Wave Functions and Superconformal Indices
• New Seiberg Dualities from N=2 Dualities
• N=1 dynamics with T_N theory
• A review of the T_N theory and its cousins
• Higher Spins and Yangian Symmetries
• M-Theory Reconstruction from (2,0) CFT and the Chiral Algebra Conjecture
• Rotating Black Hole Entropy from M5-branes
• Argyres-Douglas Theories and S-Duality
• Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals
• Macdonald Index and Chiral Algebra
• Modular anomaly equation, heat kernel and S-duality in N=2 theories
• On the large R-charge $\mathcal{N}=2$ chiral correlators and the Toda equation
• 2d TQFT structure of the superconformal indices with outer-automorphism twists
• N=2 S-duality Revisited
• Nekrasov prepotential with fundamental matter from the quantum spin chain
• Worldsheet Realization of the Refined Topological String
• Exploring ${\mathcal{W}}_{\infty }$ in the quadratic basis
• 5D SYM and 2D q-Deformed YM
• Extremal Correlators and Random Matrix Theory
• Bilinear equations on Painleve tau functions from CFT
• The Superconformal Index of the (2,0) Theory with Defects
• An Index Formula for Supersymmetric Quantum Mechanics
• Integrability and cycles of deformed $\mathcal{N}=2$ gauge theory
• Gauge/Liouville Triality
• Colored HOMFLY polynomials as multiple sums over paths or standard Young tableaux
• 5D SYM on 3D Sphere and 2D YM
• Cluster integrable systems, q-Painleve equations and their quantization
• Virasoro vacuum block at next-to-leading order in the heavy-light limit
• Revisiting the classifications of 6d SCFTs and LSTs
• Kerr-de Sitter Greybody Factors via Isomonodromy
• Semiclassical Analysis of the 3d/3d Relation
• Symmetry enhancement and closing of knots in 3d/3d correspondence
• 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
• Seiberg-Witten geometries for Coulomb branch chiral rings which are not freely generated
• Quantum curves for Hitchin fibrations and the Eynard-Orantin theory
• Toric Calabi-Yau threefolds as quantum integrable systems. R-matrix and RTT relations
• Charting Class ${\mathcal{S}}_k$ Territory
• Aspects of Defects in 3d-3d Correspondence
• On colored HOMFLY polynomials for twist knots
• RG flows with supersymmetry enhancement and geometric engineering
• 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
• F-Theory and N=1 SCFTs in Four Dimensions
• Coherent states in quantum ${\mathcal{W}}_{1+\infty }$ algebra and qq-character for 5d Super Yang-Mills
• From 3d dualities to 2d free field correlators and back
• The superconformal index and an elliptic algebra of surface defects
• Five-dimensional Chern-Simons terms and Nekrasov's instanton counting
• Line Defects, Tropicalization, and Multi-Centered Quiver Quantum Mechanics
• Free Field Realizations from the Higgs Branch
• Quantum Higgs branches of isolated N=2 superconformal field theories
• Seiberg-Witten Geometries Revisited
• On Gauge Theory and Topological String in Nekrasov-Shatashvili Limit
• Borel summability of perturbative series in 4d N=2 and 5d N=1 theories
• Check of AGT Relation for Conformal Blocks on Sphere
• Bases in coset conformal field theory from AGT correspondence and Macdonald polynomials at the roots of unity
• Null vectors, 3-point and 4-point functions in conformal field theory
• Reflection states in Ding-Iohara-Miki algebra and brane-web for D-type quiver
• Massive Scaling Limit of beta-Deformed Matrix Model of Selberg Type
• On 3d extensions of AGT relation
• Two-dimensional categorified Hall algebras
• The Liouville side of the Vortex
• Gauge Theory Wilson Loops and Conformal Toda Field Theory
• Matrix models for irregular conformal blocks and Argyres-Douglas theories
• Towards R-matrix construction of Khovanov-Rozansky polynomials. I. Primary $T$-deformation of HOMFLY
• Emergent 3-manifolds from 4d Superconformal Indices
• From SO/Sp instantons to W-algebra blocks
• The toroidal block and the genus expansion
• F-theoretic vs microscopic description of a conformal N=2 SYM theory
• W_3 irregular states and isolated N=2 superconformal field theories
• Elliptic Blowup Equations for 6d SCFTs. II: Exceptional Cases
• Quiver elliptic W-algebras
• Spectral dualities in XXZ spin chains and five dimensional gauge theories
• Kernel function and quantum algebras
• Relating Gauge Theories via Gauge/Bethe Correspondence
• Resolvents and Seiberg-Witten representation for Gaussian beta-ensemble
• N=2 S-duality via Outer-automorphism Twists
• Instanton partition functions in N=2 SU(N) gauge theories with a general surface operator, and their W-algebra duals
• SCFT/VOA correspondence via $\Omega$-deformation
• N=1 conformal dualities
• Decomposing Nekrasov Decomposition
• Hitchin Equation, Singularity, and N=2 Superconformal Field Theories
• Generalized Jack polynomials and the AGT relations for the $SU(3)$ group
• Large $N$ correlation functions in $\mathcal{N}=2$ superconformal quivers
• Sequencing BPS Spectra
• Kerr-de Sitter Quasinormal Modes via Accessory Parameter Expansion
• Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics
• Transformations of Spherical Blocks
• The general M5-brane superconformal index
• Holomorphic blocks and the 5d AGT correspondence
• A "Lagrangian" for the E7 Superconformal Theory
• AdS5 solutions from M5-branes on Riemann surface and D6-branes sources
• Conformal blocks from Wilson lines with loop corrections
• Intersecting Surface Defects and Two-Dimensional CFT
• Magnetic expansion of Nekrasov theory: the SU(2) pure gauge theory
• Towards a 4d/2d correspondence for Sicilian quivers
• Supersymmetric gauge theory, (2,0) theory and twisted 5d Super-Yang-Mills
• Chiral theories of class S
• Holographic Uniformization
• N=2 gauge theories on the hemisphere $H{S}^4$
• Supersymmetric AdS3 X S2 M-theory geometries with fluxes
• Parafermionic Liouville field theory and instantons on ALE spaces
• Analysis of correlation functions in Toda theory and AGT-W relation for SU(3) quiver
• On S-duality of the Superconformal Index on Lens Spaces and 2d TQFT
• A finite analog of the AGT relation I: finite W-algebras and quasimaps' spaces
• Intersecting Surface Defects and Instanton Partition Functions
• Exponential Networks and Representations of Quivers
• On differential equation on four-point correlation function in the Conformal Toda Field Theory
• Exact WKB and abelianization for the $T_3$ equation
• Irregular conformal blocks, with an application to the fifth and fourth Painlevé equations
• N=1 Superpotentials from Multi-Instanton Calculus
• 2d-4d Connection between q-Virasoro/W Block at Root of Unity Limit and Instanton Partition Function on ALE Space
• Equations on knot polynomials and 3d/5d duality
• Precision Microstate Counting for the Entropy of Wrapped M5-branes
• Non-Perturbative Nekrasov Partition Function from String Theory
• Wilson Loops and Chiral Correlators on Squashed Sphere
• New N=1 Dualities from M5-branes and Outer-automorphism Twists
• Surface defects and instanton-vortex interaction
• Surface defects and elliptic quantum groups
• Twisting with a Flip (the Art of Pestunization)
• Quarter-BPS AdS5 solutions in M-theory with a T2 bundle over a Riemann surface
• Global Supersymmetry on Curved Spaces in Various Dimensions
• Colored Kauffman Homology and Super-A-polynomials
• Surface defects, the superconformal index and q-deformed Yang-Mills
• Chiral algebras from Ω-deformation
• An M-Theoretic Derivation of a 5d and 6d AGT Correspondence, and Relativistic and Elliptized Integrable Systems
• N=2 gauge theories on toric singularities, blow-up formulae and W-algebrae
• 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
• Triality in Little String Theories
• Spectral duality in elliptic systems, six-dimensional gauge theories and topological strings
• Fractional quiver W-algebras
• Quantization condition from exact WKB for difference equations
• Superconformal Index with Duality Domain Wall
• Holographic entanglement entropy from probe M-theory branes
• Blowup Equations for Refined Topological Strings
• AGT, Burge pairs and minimal models
• Instanton R-matrix and W-symmetry
• An elliptic Virasoro symmetry in 6d
• Non-Perturbative Topological Strings And Conformal Blocks
• Confluent conformal blocks and the Teukolsky master equation
• Hilbert Series for Moduli Spaces of Instantons on C^2/Z_n
• 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
• Holography of 3d-3d correspondence at Large N
• Reflection Amplitudes in Non-Simply Laced Toda Theories and Thermodynamic Bethe Ansatz
• Tinkertoys for the E7 Theory
• From 6D SCFTs to Dynamic GLSMs
• Linear Quivers and N=1 SCFTs from M5-branes
• Deformed Seiberg-Witten Curves for ADE Quivers
• Bootstrapping line defects in $\mathcal{N}=2$ theories
• Self-dual strings in six dimensions: Anomalies, the ADE-classification, and the world-sheet WZW-model
• 3d-3d Correspondence Revisited
• $\mathcal{N}=2$ conformal gauge theories at large R-charge: the $SU(N)$ case
• N=1 Geometries via M-theory
• Modular anomaly equations in N=2* theories and their large-N limit
• Chiral Algebras, Localization and Surface Defects
• Quantum Holonomies from Spectral Networks and Framed BPS States
• From Brezin-Hikami to Harer-Zagier formulas for Gaussian correlators
• Selberg Integral and SU(N) AGT Conjecture
• ADE Spectral Networks
• On elementary proof of AGT relations from six dimensions
• Quantum geometry of moduli spaces of local systems and representation theory
• The large central charge limit of conformal blocks
• Genus-one correction to asymptotically free Seiberg-Witten prepotential from Dijkgraaf-Vafa matrix model
• Classical irregular block, N=2 pure gauge theory and Mathieu equation
• Sequences of $6d$ SCFTs on generic Riemann surfaces
• The vertex algebras ${\mathcal{R}}^{(p)}$ and ${\mathcal{V}}^{(p)}$
• Landscape of Simple Superconformal Field Theories in 4d
• New Directions in Bipartite Field Theories
• Unoriented Quivers with Flavour
• Wilson Surface Central Charge from Holographic Entanglement Entropy
• On genus expansion of superpolynomials
• On 6d N=(2,0) theory compactified on a Riemann surface with finite area
• Hitchin Equation, Irregular Singularity, and $N=2$ Asymptotical Free Theories
• Holographic duals of large-c torus conformal blocks
• On Extensions of $\widehat{\mathfrak{gl}(m|n)}$ Kac-Moody algebras and Calabi-Yau Singularities
• Isomonodromic $\tau$-functions and $W_N$ conformal blocks
• The Singularity Structure of Scale-Invariant Rank-2 Coulomb Branches
• ADE Little String Theory on a Riemann Surface (and Triality)
• On the 5d instanton index as a Hilbert series
• BPS States in Omega Background and Integrability
• Higher laminations, webs and N=2 line operators
• Toda Theory From Six Dimensions
• Teichmuller TQFT vs Chern-Simons Theory
• Generalized Hitchin system, Spectral curve and N=1 dynamics
• BPS Graphs: From Spectral Networks to BPS Quivers
• Torus HOMFLY as the Hall-Littlewood Polynomials
• Double scaling limit of N=2 chiral correlators with Maldacena-Wilson loop
• Aspects of $\Omega$-deformed M-theory
• The Threebrane Soliton of the M-Fivebrane
• Six-dimensional Origin of $\mathcal{N}=4$ SYM with Duality Defects
• M-Theoretic Derivations of 4d-2d Dualities: From a Geometric Langlands Duality for Surfaces, to the AGT Correspondence, to Integrable Systems
• 3d-3d correspondence for mapping tori
• Unification of integrability in supersymmetric gauge theories
• Classical conformal blocks from TBA for the elliptic Calogero-Moser system
• Superconformal Index and 3d-3d Correspondence for Mapping Cylinder/Torus
• N=2 SU Quiver with USP Ends or SU Ends with Antisymmetric Matter
• 't Hooft Operators in Gauge Theory from Toda CFT
• On AGT description of N=2 SCFT with N_f=4
• Shift versus Extension in Refined Partition Functions
• Mayer-Cluster Expansion of Instanton Partition Functions and Thermodynamic Bethe Ansatz
• New N=1 dualities from orientifold transitions - Part I: Field Theory
• Conformal blocks of W_N Minimal Models and AGT correspondence
• Deformed supersymmetric gauge theories from the fluxtrap background
• Large $N$ twisted partition functions in 3d-3d correspondence and Holography
• Supersymmetric Gauge Theories on a Squashed Four-Sphere
• (q,t)-KZ equation for Ding-Iohara-Miki algebra
• Superconformal field theory and Jack superpolynomials
• New N=1 dualities from orientifold transitions - Part II: String Theory
• Matrix model from N = 2 orbifold partition function
• Coulomb branches with complex singularities
• SH${}^c$ Realization of Minimal Model CFT: Triality, Poset and Burge Condition
• Generalized matrix models and AGT correspondence at all genera
• Universal two-parameter ${\mathcal{W}}_{\infty }$-algebra and vertex algebras of type $\mathcal{W}(2,3,\dots ,N)$
• On W-algebras and the symmetries of defects of 6d N=(2,0) theory
• Quantizing higher-spin gravity in free-field variables
• Introduction to localization in quantum field theory
• Splitting of surface defect partition functions and integrable systems
• 2-parameter $\tau$-function for the first Painlevé equation -Topological recursion and direct monodromy problem via exact WKB analysis-
• Moore-Read Fractional Quantum Hall wavefunctions and SU(2) quiver gauge theories
• Liouville theory, N=2 gauge theories and accessory parameters
• $q$-Virasoro/W Algebra at Root of Unity and Parafermions
• A2 Toda theory in reduced WZNW framework and the representations of the W algebra
• Construction of Gaiotto states with fundamental multiplets through Degenerate DAHA
• Schur sector of Argyres-Douglas theory and $W$-algebra
• Braided Tensor Categories related to ${\mathcal{B}}_p$ Vertex Algebras
• Higgsed network calculus
• Rationalizing CFTs and Anyonic Imprints on Higgs Branches
• Quiver gauge theories and integrable lattice models
• N=2 gauge theories and quantum phases
• On AGT-W Conjecture and q-Deformed W-Algebra
• Punctures for Theories of Class ${\mathcal{S}}_{\Gamma }$
• An introduction to supersymmetric field theories in curved space
• The Stringy Instanton Partition Function
• 4d Quantum Geometry from 3d Supersymmetric Gauge Theory and Holomorphic Block
• Scheme dependence of instanton counting in ALE spaces
• Argyres-Douglas theories, Painlevé II and quantum mechanics
• Crystallization of deformed Virasoro algebra, Ding-Iohara-Miki algebra and 5D AGT correspondence
• On determinant representation and integrability of Nekrasov functions
• Five-dimensional SU(2) AGT conjecture and recursive formula of deformed Gaiotto state
• On 't Hooft Defects, Monopole Bubbling and Supersymmetric Quantum Mechanics
• S-duality as Fourier transform for arbitrary ${\epsilon }_1,{\epsilon }_2$
• R-matrix-valued Lax pairs and long-range spin chains
• $q$-Virasoro modular double and 3d partition functions
• Perturbative and nonperturbative aspects of complex Chern-Simons Theory
• Two-point correlators in non-conformal $\mathcal{N}=2$ gauge theories
• On the chiral algebra of Argyres-Douglas theories and S-duality
• An N=1 Lagrangian for the rank 1 E6 superconformal theory
• On the crossing relation in the presence of defects
• Line defects and (framed) BPS quivers
• N=2 Gauge Theories: Congruence Subgroups, Coset Graphs and Modular Surfaces
• SUSY enhancement from T-branes
• S-Duality and Modular Transformation as a non-perturbative deformation of the ordinary pq-duality
• Trisecting non-Lagrangian theories
• Reflection Amplitudes of ADE Toda Theories and Thermodynamic Bethe Ansatz
• A search for AdS5 X S2 IIB supergravity solutions dual to N = 2 SCFTs
• Integrability from 2d N=(2,2) Dualities
• Classical Conformal Blocks and Accessory Parameters from Isomonodromic Deformations
• W(1+infinity) algebra as a symmetry behind AGT relation
• Compactification on the Ω-background and the AGT correspondence
• Refined geometric transition and $qq$-characters
• Chern-Simons theory from M5-branes and calibrated M2-branes
• Gauge theories on compact toric surfaces, conformal field theories and equivariant Donaldson invariants
• N=1 curves for trifundamentals
• AGT, N-Burge partitions and W_N minimal models
• Heterotic Surface Defects and Dualities from 2d/4d Indices
• Ω-deformation of B-twisted gauge theories and the 3d-3d correspondence
• Comparing Instanton Contributions with Exact Results in N=2 Supersymmetric Scale Invariant Theories
• The moduli space of instantons on an ALE space from 3d $\mathcal{N}=4$ field theories
• Four-dimensional Lens Space Index from Two-dimensional Chiral Algebra
• Holography of Wrapped M5-branes and Chern-Simons theory
• On the Correspondence between Surface Operators in Argyres-Douglas Theories and Modules of Chiral Algebra
• Instantons from Blow-up
• Factorization of differential expansion for antiparallel double-braid knots
• Smallest 3d hyperbolic manifolds via simple 3d theories
• Flavored surface defects in 4d N=1 SCFTs
• A 3d-3d appetizer
• A brief review of the 2d/4d correspondences
• 3d N=2 Theories from Cluster Algebras
• Theories of Class F and Anomalies
• Holomorphic field realization of SH${}^c$ and quantum geometry of quiver gauge theories
• The moduli space of vacua of N=2 class S theories
• Tinkertoys for the Twisted $E_6$ Theory
• Equivariant Verlinde algebra from superconformal index and Argyres-Seiberg duality
• Four dimensional superconformal theories from M5 branes
• Line defect Schur indices, Verlinde algebras and $U(1{)}_r$ fixed points
• CFT exercises for the needs of AGT
• Aspects of line operators of class S theories
• β-deformed matrix model and Nekrasov partition function
• From Liouville to Chern-Simons, Alternative Realization of Wilson Loop Operators in AGT Duality
• Seiberg-Witten curve via generalized matrix model
• Complete solution to Gaussian tensor model and its integrable properties
• Exact Deconstruction of the 6D (2,0) Theory
• N=2 SUSY gauge theories on S^4
• Quantum geometry from the toroidal block
• On spectrum of ILW hierarchy in conformal field theory II: coset CFT's
• S-duality in $\mathcal{N}=1$ orientifold SCFTs
• Geometry of Higgs-branch superconformal primary bundles
• Class $\mathcal{S}$ Anomalies from M-theory Inflow
• Surface defects in E-string compactifications and the van Diejen model
• Virasoro constraint for Nekrasov instanton partition function
• A note on the algebraic engineering of 4D $\mathcal{N}=2$ super Yang-Mills theories
• New quantum toroidal algebras from 5D $\mathcal{N}=1$ instantons on orbifolds
• Ellipsoid partition function from Seiberg-Witten monopoles
• On the $K$-theoretic Hall algebra of a surface
• On $W$-representations of $\beta$- and $q,t$-deformed matrix models
• A note on the Virasoro blocks at order $1/c$
• N=2 quiver gauge theories on A-type ALE spaces
• Supersymmetric backgrounds from 5d N=1 supergravity
• Punctures from Probe M5-Branes and N=1 Superconformal Field Theories
• $\mathcal{N}=1$ superconformal theories with $D_N$ blocks
• Seiberg-Witten curves and double-elliptic integrable systems
• On modular transformations of non-degenerate toric conformal blocks
• 2D CFT blocks for the 4D class ${\mathcal{S}}_k$ theories
• Argyres-Douglas matter and N=2 dualities
• Infrared enhancement of supersymmetry in four dimensions
• Correlation functions with fusion-channel multiplicity in W3 Toda field theory
• $\mathcal{N}=2^{\ast }$ gauge theory, free fermions on the torus and Painlevé VI
• Bethe subalgebras of quantum affine gl(n) via shuffle algebras
• Surface defects as transfer matrices
• WKB Method and Quantum Periods beyond Genus One
• Coset conformal field theory and instanton counting on C^2/Z_p
• Large N limit of beta-ensembles and deformed Seiberg-Witten relations
• Uniformization, Calogero-Moser/Heun duality and Sutherland/bubbling pants
• Classical Virasoro irregular conformal block
• W-algebras and surface operators in N=2 gauge theories
• Classification of N=2 Superconformal Field Theories with Two-Dimensional Coulomb Branches, II
• Backlund transformation of Painleve III($D_8$) tau function
• Structure of Anomalies of 4d SCFTs from M5-branes, and Anomaly Inflow
• Universality of Toda equation in $\mathcal{N}=2$ superconformal field theories
• Virasoro irregular conformal block and beta deformed random matrix model
• Homomorphisms between different quantum toroidal and affine Yangian algebras
• Quantum curves and conformal field theory
• New S-dualities in N=2 supersymmetric SU(2) x SU(2) gauge theory
• Comments on knotted 1/2 BPS Wilson loops
• TBA for non-perturbative moduli spaces
• Alpha- and Omega-Deformations from fluxes in M-Theory
• Minimal lectures on two-dimensional conformal field theory
• Discrete Painleve system and the double scaling limit of the matrix model for irregular conformal block and gauge theory
• Bands and gaps in Nekrasov partition function
• Large N techniques for Nekrasov partition functions and AGT conjecture
• Generalized Whittaker states for instanton counting with fundamental hypermultiplets
• Superconformal minimal models and admissible Jack polynomials
• Maulik-Okounkov's R-matrix from Ding-Iohara-Miki algebra
• Fiber-base duality from the algebraic perspective
• Homological Classification of 4d $\mathcal{N}=2$ QFT. Part I: Rank-1 revisited
• Monopole Bubbling via String Theory
• Quantum periods and prepotential in $\mathcal{N}=2$ SU(2) SQCD
• 4d partition function on S^1 x S^3 and 2d Yang-Mills with nonzero area
• ε-Corrected Seiberg-Witten Prepotential Obtained From Half Genus Expansion in beta-Deformed Matrix Model
• Modular and duality properties of surface operators in N=2* gauge theories
• Quantum Cohomology and Quantum Hydrodynamics from Supersymmetric Quiver Gauge Theories
• An $\mathcal{N}=1$ 3d-3d Correspondence
• Argyres-Douglas matter and S-duality: Part II
• Refined matrix models from BPS counting
• AGT/Z${}_2$
• On the six-dimensional origin of the AGT correspondence
• Refined 3d-3d Correspondence
• Lifshitz Scaling, Microstate Counting from Number Theory and Black Hole Entropy
• Lecture notes on Liouville theory and the DOZZ formula
• Macdonald topological vertices and brane condensates
• From Jack polynomials to minimal model spectra
• (de)Tails of Toda CFT
• On the Jeffrey-Kirwan residue of BCD-instantons
• AGT conjecture and AFLT states: a complete construction
• Discrete Painleve system for the partition function of $N_f=2$ $SU(2)$ supersymmetric gauge theory and its double scaling limit
• Classical Virasoro irregular conformal block II
• Indices for 6 dimensional superconformal field theories
• Confinement and Mayer cluster expansions
• On Monopole Bubbling Contributions to 't Hooft Loops
• Free fermions, W-algebras and isomonodromic deformations
• Network, cluster coordinates and N = 2 theory II: Irregular singularity
• Star shaped quivers with flux
• Accessory parameters for Liouville theory on the torus
• Several realizations of Fock modules for quantum toroidal algebras of sl(n)
• Membrane Quantum Mechanics
• N=1 superconformal blocks with Ramond fields from AGT correspondence
• 3d Expansions of 5d Instanton Partition Functions
• Argyres-Douglas theories and Liouville Irregular States
• An Elliptic Vertex of Awata-Feigin-Shiraishi type for M-strings
• Type-B Anomaly Matching and the 6D (2,0) Theory
• M5-brane Defect and QHE in AdS_4 x N(1,1)/N=3 SCFT
• Scaling dimensions of Coulomb branch operators of 4d N=2 superconformal field theories
• 3d $\mathcal{N}=2$ minimal SCFTs from Wrapped M5-branes
• Cauchy formula and the character ring
• Comment on integrability in Dijkgraaf-Vafa beta-ensembles
• CFT approach to the $q$-Painlevé VI equation
• On Higgs Branch Localization of Seiberg-Witten Theories on Ellipsoid
• Web Construction of ABCDEFG and Affine Quiver Gauge Theories
• Flowing from 16 to 32 Supercharges
• Classical limit of irregular blocks and Mathieu functions
• Comments on the twisted punctures of $A_{\text{even}}$ class S theory
• S-duality, triangle groups and modular anomalies in N=2 SQCD
• Elliptic recursion for 4-point superconformal blocks and bootstrap in N=1 SLFT
• Symmetry enhancements via 5d instantons, qW-algebrae and (1,0) superconformal index
• Lax matrix solution of c=1 Conformal Field Theory
• Partition functions of web diagrams with an O7${}^{-}$-plane
• Wilson Loops and Chiral Correlators on Squashed Spheres
• Gluing two affine Yangians of ${\mathfrak{gl}}_1$
• Non-perturbative studies of N=2 conformal quiver gauge theories
• Quasimodular instanton partition function and the elliptic solution of Korteweg-de Vries equations
• Construction and Deconstruction of Single Instanton Hilbert Series
• Taming Supersymmetric Defects in 3d-3d Correspondence
• M5-branes on S^2 x M_4: Nahm's Equations and 4d Topological Sigma-models
• Finite ${\epsilon }_2$-corrections to the $\mathcal{N}=2$ SYM prepotential
• 't Hooft Defects and Wall Crossing in SQM
• On Factorization of Generalized Macdonald Polynomials
• Spherical Hecke algebra in the Nekrasov-Shatashvili limit
• Plane Partition Realization of (Web of) W-algebra Minimal Models
• Quantum periods for $\mathcal{N}=2$ $SU(2)$ SQCD around the superconformal point
• Super instanton counting and localization
• Baxter's T-Q equation, SU(N)/SU(2)^{N-3} correspondence and Ω-deformed Seiberg-Witten prepotential
• Parametric dependence of irregular conformal block
• Holographic Surface Defects in $D=5$, $N=4$ Gauged Supergravity
• On Elliptic Algebras and Large-n Supersymmetric Gauge Theories
• Exact results in N=2 gauge theories
• The BPS Spectrum Generator In 2d-4d Systems
• Irregular conformal block, spectral curve and flow equations
• A note on Wilson-'t Hooft operators
• A Macdonald refined topological vertex
• BPS M5-branes as Defects for the 3d-3d Correspondence
• An elliptic topological vertex
• Classification of N=2 Superconformal Field Theories with Two-Dimensional Coulomb Branches
• $\mathcal{N}=2^{\star }$ from Topological Amplitudes in String Theory
• Superconformal index with surface defects for class ${\mathcal{S}}_k$
• On Integrable Structure and Geometric Transition in Supersymmetric Gauge Theories
• Generalized Macdonald Functions on Fock Tensor Spaces and Duality Formula for Changing Preferred Direction
• Super-Liouville - Double Liouville correspondence
• On exclusive Racah matrices $\bar{S}$ for rectangular representations
• Combinatorial expressions for the tau functions of $q$-Painlevé V and III equations
• Recursive Method for Nekrasov partition function for classical Lie groups
• On the large $\Omega$-deformations in the Nekrasov-Shatashvili limit of $\mathcal{N}=2^{\ast }$ SYM
• The M-theory origin of global properties of gauge theories
• q-Painleve equation from Virasoro constraints
• OPE Selection Rules for Schur Multiplets in 4D $\mathcal{N}=2$ Superconformal Field Theories
• A quantum isomonodromy equation and its application to N=2 SU(N) gauge theories
• N=2 gauge theories, instanton moduli spaces and geometric representation theory
• Elliptic modular double and 4d partition functions
• Omega-Deformed Seiberg-Witten Effective Action from the M5-brane
• On a singular Fredholm-type integral equation arising in N=2 super Yang-Mills theories
• $T$, $Q$ and periods in $SU(3)$ $\mathcal{N}=2$ SYM
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• q-Vertex Operator from 5D Nekrasov Function
• Liouville's Imaginary Shadow
• Higher AGT Correspondences, W-algebras, and Higher Quantum Geometric Langlands Duality from M-Theory
• Resurgence, Painleve Equations and Conformal Blocks
• Junctions of surface operators and categorification of quantum groups
• Seiberg-Witten geometry of four-dimensional N=2 SO-USp quiver gauge theories, I
• N=2 superconformal blocks and instanton partition functions
• Bootstrapping the $S^5$ partition function
• Quantum Hall Effect and Langlands Program
• Chiral observables and S-duality in N = 2* U(N) gauge theories
• Impure Aspects of Supersymmetric Wilson Loops
• Correspondences between WZNW models and CFTs with W-algebra symmetry
• Localization of a supersymmetric gauge theory in the presence of a surface defect
• On the Integrability of Four Dimensional N=2 Gauge Theories in the Omega Background
• Higher rank isomonodromic deformations and W-algebras
• Trinion Conformal Blocks from Topological strings
• Quantum integrability from non-simply laced quiver gauge theory
• Generalized Rogers Ramanujan Identities from AGT Correspondence
• Seiberg-Witten for $Spin(n)$ with Spinors
• Second level semi-degenerate fields in W3 Toda theory: matrix element and differential equation
• Notes on Mayer Expansions and Matrix Models
• Combinatorial approach to Mathieu and Lamé equations
• Integrating over quiver variety and BPS/CFT correspondence
• Off-shell structure of twisted (2,0) theory
• On Quiver W-algebras and Defects from Gauge Origami
• A freely generated ring for N=1 models in class S_k
• Equivariant volumes of non-compact quotients and instanton counting
• Toward the Pole
• 5d gauge theories on orbifolds and 4d 't Hooft line indices
• Testing Macdonald Index as a Refined Character of Chiral Algebra
• Exact conformal blocks for the W-algebras, twist fields and isomonodromic deformations
• Exact partition functions for the $\Omega$-deformed $\mathcal{N}=2^{\ast }$ $SU(2)$ gauge theory
• Quiver ${\text{W}}_{{\epsilon }_1,{\epsilon }_2}$ algebras of 4d $\mathcal{N}=2$ gauge theories
• AFLT-type Selberg integrals
• N = 2 SCFTs: An M5-brane perspective
• Exts and the AGT relations
• Recurrence relations for the ${\mathcal{W}}_3$ conformal blocks and $\mathcal{N}=2$ SYM partition functions
• Surface Operators from M-strings
• Gluing affine Yangians with bi-fundamentals
• Wall-crossing, open BPS counting and matrix models
• ABCD of Beta Ensembles and Topological Strings
• Existence and Orthogonality of Generalized Jack Polynomials and Its $q$-Deformation
• The ABCDEFG of Little Strings
• Exact SUSY Wilson loops on $S^3$ from $q$-Virasoro constraints
• VEV of Baxter's Q-operator in N=2 gauge theory and the BPZ differential equation
• Some remarks on D-branes and defects in Liouville and Toda field theories
• Duality walls in the 4d N=2 SU(N) gauge theory with 2N flavours
• Mayer expansion of the Nekrasov pre potential: the subleading ${\epsilon }_2$-order
• Resumming perturbative series in the presence of monopole bubbling effects
• Condensates and instanton - torus knot duality. Hidden Physics at UV scale
• BPS states in the Omega-background and torus knots
• Rigid Fuchsian systems in 2-dimensional conformal field theories
• Residue Formulas for Prepotentials, Instanton Expansions and Conformal Blocks
• Check-Operators and Quantum Spectral Curves
• Little String Defects and Bala-Carter Theory
• AGT relation in the light asymptotic limit
• On Hamiltonians for Kerov functions
• Classical irregular blocks, Hill's equation and PT-symmetric periodic complex potentials
• The Holographic Dual of the $\Omega$-background
• Confinement and duality in supersymmetric gauge theories
• A note on S-dual basis in free fermion system
• Non-integrability of the $\Omega$-deformation
• Tau-functions for Quiver Gauge Theories
• Twist-field representations of W-algebras, exact conformal blocks and character identities
• 5D SYM on 3D Deformed Spheres
• Multicritical points of unitary matrix model with logarithmic potential identified with Argyres-Douglas points
• Deconstructing Little Strings with $\mathcal{N}=1$ Gauge Theories on Ellipsoids
• Little String Origin of Surface Defects
• Super-Yang-Mills theories on S4 x R
• Norms of logarithmic primaries of Virasoro algebra
• Chiral trace relations in $\Omega$-deformed $\mathcal{N}=2$ theories
• Refined toric branes, surface operators and factorization of generalized Macdonald polynomials
• Discrete Integrable Systems, Supersymmetric Quantum Mechanics, and Framed BPS States - I
• Kac determinant and singular vector of the level N representation of Ding-Iohara-Miki algebra
• Line operators from M-branes on compact Riemann surfaces
• Resumming instantons in N=2* theories with arbitrary gauge groups
• Superconformal Quantum Mechanics from M2-branes
• On solutions of the Fuji-Suzuki-Tsuda system
• Mirror of the refined topological vertex from a matrix model
• On some 3-point functions in the $W_4$ CFT and related braiding matrix
• Cluster integrable systems and spin chains
• Conformal blocks of Chiral fields in N=2 SUSY CFT and Affine Laumon Spaces
• Generalization and Deformation of Drinfeld quantum affine algebras
• Hitchin systems in N=2 field theory
• Pentad and triangular structures behind the Racah matrices
• The Condensate from Torus Knots
• Holomorphic Anomaly in Gauge Theory on ALE space
• Seiberg-Witten equations and non-commutative spectral curves in Liouville theory
• Argyres-Douglas Loci, Singularity Structures and Wall-Crossings in Pure N=2 Gauge Theories with Classical Gauge Groups
• On generalized Macdonald polynomials
• The trouble with twisting (2,0) theory
• Unifying Lattice Models, Links and Quantum Geometric Langlands via Branes in String Theory
• The gravity duals of SO/USp superconformal quivers
• Refined topological vertex for a 5D $Sp(N)$ gauge theory with antisymmetric matter
• Analytic properties of the Virasoro modular kernel
• Comments on fusion matrix in N=1 super Liouville field theory
• Equivariant U(N) Verlinde algebra from Bethe/Gauge correspondence
• N=2 supersymmetric QCD and elliptic potentials
• An(1) Affine Quiver Matrix Model
• Faces of matrix models
• Unitary matrix with a Penner-like potential also yields N_f=2
• S-duality wall of SQCD from Toda braiding
• Introduction to double Hecke algebras
• Irregular matrix model with $\mathcal{W}$ symmetry
• Entanglement in Theory Space
• Two-dimensional superconformal field theories from Riemann surfaces with boundary
• Refined Cigar and Omega-deformed Conifold
• Index-Like Theorems from Line Defect Vevs
• Wall-crossing and operator ordering for 't Hooft operators in N=2 gauge theories
• (0,2) Dualities and the 4-Simplex
• On Dimensional Transmutation in 1+1D Quantum Hydrodynamics
• An infrared bootstrap of the Schur index with surface defects
• Hyperbolic deformation of the strip-equation and the accessory parameters for the torus
• Wilson Loop Invariants from $W_N$ Conformal Blocks
• Quivers, Line Defects and Framed BPS Invariants
• Irregular Vertex Operators for Irregular Conformal Blocks
• Quantum Line Defects and Refined BPS Spectra
• Cut-and-join operators and Macdonald polynomials from the 3-Schur functions
• Irregular Singularities in the H3+ WZW Model
• From topological strings to minimal models
• Notes on 3-point functions of A_{N-1} Toda theory and AGT-W relation for SU(N) quiver
• Twisted reduction of quiver W-algebras
• Deconstructing Defects
• Describing codimension two defects
• Exact partition functions for deformed $\mathcal{N}=2$ theories with $N_f=4$ flavours
• Deformed Virasoro algebras from elliptic quantum algebras
• $\widehat{\mathfrak{sl}}(n{)}_N$ WZW conformal blocks from $SU(N)$ instanton partition functions on ${\mathbb{C}}^2/{\mathbb{Z}}_n$
• Double quantization of Seiberg-Witten geometry and W-algebras
• Penner Type Ensemble for Gauge Theories Revisited
• Quantum spectral curve for (q,t)-matrix model
• Classical Liouville Three-point Functions from Riemann-Hilbert Analysis
• On even spin $W_{\infty }$
• Elliptic Genus Derivation of 4d Holomorphic Blocks
• Pentagon identities arising in supersymmetric gauge theory computations
• FQHE and $t{t}^{\ast }$ geometry
• S duality and Framed BPS States via BPS Graphs
• Classical limits of quantum toroidal and affine Yangian algebras
• Note on refined topological vertex, Jack polynomials and instanton counting
• Quantum integrability of $\mathcal{N}=2$ 4d gauge theories
• Integrability in non-perturbative QFT
• Topological AdS/CFT and the $\Omega$ deformation
• A strange relationship between 2d CFT and 4d gauge theory
• Genus one correction to Seiberg-Witten prepotential from β-deformed matrix model
• Irregular conformal block and its matrix model
• A new treatment for some periodic Schrödinger operators II: the wave function
• Spinless basis for spin-singlet FQH states
• c-Recursion for multi-point superconformal blocks. NS sector
• Nekrasov and Argyres-Douglas theories in spherical Hecke algebra representation
• Recursions in Calogero-Sutherland Model Based on Virasoro Singular Vectors
• Generalized hypergeometric series for Racah matrices in rectangular representations
• Kähler Uniformization from Holographic Renormalization Group Flows of M5-branes
• Wilson punctured network defects in 2D q-deformed Yang-Mills theory
• Fractional Quantum Hall Effect and M-Theory
• Partition Functions of $\mathcal{N}=1$ Gauge Theories on $S^2\times {\mathbb{R}}_{\epsilon }^2$ and Duality
• Geometric transitions, double scaling limits and gauge theories
• On new exact conformal blocks and Nekrasov functions
• Discrete Painleve equation, Miwa variables, and string equation in 5d matrix models
• Cohomological Hall algebra of Higgs sheaves on a curve
• Seiberg-Witten period relations in Omega background
• The Geometry of SUSY Enhancement
• Second Order RG Flow in General su(2) Coset Models
• Cubic constraints for the resolvents of the ABJM matrix model and its cousins
• Spectra of elliptic potentials and supersymmetric gauge theories
• Vertex Operators for Irregular Conformal Blocks: Supersymmetric Case
• Magnetically charged AdS5 black holes from class S theories on hyperbolic 3-manifolds
• Deformed planar topological open string amplitudes on Seiberg-Witten curve
• BPZ equations for higher degenerate fields and nonperturbative Dyson-Schwinger equations
• Aspects of the moduli space of instantons on $\mathbb{C}{P}^2$ and its orbifolds
• Construction of 4d SYM compactified on open Riemann surfaces by the superfield formalism
• The Euler anomaly and scale factors in Liouville/Toda CFTs
• Generalized Toda Theory from Six Dimensions and the Conifold
• Four-Dimensional N=2 Supersymmetric Theory with Boundary as a Two-Dimensional Complex Toda Theory
• Lens space index and global properties for 4d N = 2 models
• The light asymptotic limit of conformal blocks in $\mathcal{N}=1$ super Liouville field theory
• Cluster-Enriched Yang-Baxter Equation from SUSY Gauge Theories
• Super-spectral curve of irregular conformal blocks
• The imaginary Toda field theory
• Discrete matrix models for partial sums of conformal blocks associated to Painlevé transcendents
• On the description of surface operators in N=2* super Yang-Mills
• Orbifold Vortex and Super Liouville Theory
• 4d $\mathcal{N}=1$/2d Yang-Mills Duality in Holography
• Riemann-Hilbert treatment of Liouville theory on the torus: The general case
• Partially twisted superconformal M5 brane in R-symmetry gauge field backgrounds
• Non-perturbative aspects of gauge/gravity duality
• Representations of the Heisenberg algebra and moduli spaces of framed sheaves
• Symmetric functions in superspace: a compendium of results and open problems (including a SageMath worksheet)
• The Toda system and solution to the $\mathcal{N}$=2 SUSY Yang-Mills theory
• Hilbert schemes of nonreduced divisors in Calabi-Yau threefolds and W-algebras
• Schur indices with class S line operators from networks and further skein relations
• On resummation of the irregular conformal block
• Q-balls of Quasi-particles in a (2,0)-theory model of the Fractional Quantum Hall Effect
• $W_4$ Toda example as hidden Liouville CFT
• Vortex-strings in N=2 quiver X U(1) theories
• Elliptic algebra, Frenkel-Kac construction and root of unity limit
• Weak Coupling Limits and Colliding Punctures in Class-S Theories
• Instanton counting via affine Lie algebras II: from Whittaker vectors to the Seiberg-Witten prepotential
• Conformal field theories from deformations of theories with $W_n$ symmetry
• Dual infrared limits of 6d $\mathcal{N}$=(2,0) theory
• Coloured refined topological vertices and parafermion conformal field theories
• Localization of four-dimensional super Yang-Mills theories compactified on Riemann surface
• Interactions of Irregular Gaiotto States in Liouville Theory
• VEV of $Q$-operator in $U(1)$ linear quiver 5d gauge theories
• A note on W symmetry of N=2 gauge theory
• Super-Whittaker vector at c=3/2
• Codimension two defects and the Springer correspondence
• Chiral rings for surface operators in 4d and 5d SQCD
• A note on chiral trace relations from qq-characters
• Irregular Conformal States and Spectral Curve: Irregular Matrix Model Approach
• Non-rational su(2) cosets and Liouville field theory
• Quantum Trilogy: Discrete Toda, Y-System and Chaos
• Solvable spectral problems from 2d CFT and N=2 gauge theories
• Instanton-torus knot duality in 5d SQED and $SU(2)$ SQCD

Cited by in corpus (19)

• Holographic thermal correlators from supersymmetric instantons
• Mean string field theory: Landau-Ginzburg theory for 1-form symmetries
• Two 6d origins of 4d SCFTs: class $\mathcal{S}$ and 6d (1,0) on a torus
• Quantum toroidal algebras and solvable structures in gauge/string theory
• Observations on BPS observables in 6d
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• 5d AGT correspondence of supergroup gauge theories from quantum toroidal ${\mathfrak{gl}}_1$
• Gauge origami and quiver W-algebras
• Comments on chiral algebras and $\Omega$-deformations
• On the exponentially small corrections to $\mathcal{N}=2$ superconformal correlators at large R-charge
• Gauge origami and quiver W-algebras III: Donaldson--Thomas $qq$-characters
• Super Topological Recursion and Gaiotto Vectors For Superconformal Blocks
• Lectures on chiral algebras of $\mathcal{N}⩾2$ superconformal field theories
• Representations of quantum toroidal superalgebras and plane $\mathbf{s}$-partitions
• The thermal representation of conformal ladder integrals
• Flavor deformations and supersymmetry enhancement in $4d$ $\mathcal{N}=2$ theories
• Aspects of 4d supersymmetric dynamics and geometry
• Schur Connections: Chord Counting, Line Operators, and Indices
• Proof of 5D $A_n$ AGT conjecture at $\beta =1$