Liouville correlation functions from four-dimensional gauge theories

DOI10.1007/s11005-010-0369-5zbMath1185.81111arXiv0906.3219OpenAlexW2107702031WikidataQ56057582 ScholiaQ56057582MaRDI QIDQ2270180

Davide Gaiotto, Luis F. Alday, Yuji Tachikawa

Publication date: 15 March 2010

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0906.3219

zbMATH Keywords

conformal field theory gauge theory AGT conjecture

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Supersymmetric field theories in quantum mechanics (81T60) Yang-Mills and other gauge theories in quantum field theory (81T13) Applications of deformations of analytic structures to the sciences (32G81)

Related Items

Spectrum of quantum transfer matrices via classical many-body systems ⋮ The stringy instanton partition function ⋮ Non-Lagrangian theories from brane junctions ⋮ Exact results for Wilson loops in arbitrary representations ⋮ The trouble with twisting $(2,0)$ theory ⋮ BPS states in the $\Omega$-background and torus knots ⋮ Parametric dependence of irregular conformal block ⋮ Super-Liouville -- double Liouville correspondence ⋮ Two-dimensional crystal melting and D4-D2-D0 on toric Calabi-Yau singularities ⋮ AGT, burge pairs and minimal models ⋮ Towards $\mathcal{R}$-matrix construction of Khovanov-Rozansky polynomials I. Primary $T$-deformation of HOMFLY ⋮ Classical conformal blocks and Painlevé VI ⋮ Isomonodromy, Painlevé transcendents and scattering off of black holes ⋮ Quantum geometry from the toroidal block ⋮ Super-Yang-Mills theories on $S^4\times\mathbb R$ ⋮ Down the rabbit hole with theories of class $ \mathcal{S} $ ⋮ Alpha- and omega-deformations from fluxes in M-theory ⋮ Off-shell structure of twisted $(2,0)$ theory ⋮ $N=2$ supersymmetric QCD and elliptic potentials ⋮ Classical irregular block, $ \mathcal{N} = 2$ pure gauge theory and Mathieu equation ⋮ Holomorphic blocks in three dimensions ⋮ Mayer expansion of the Nekrasov prepotential: the subleading $\epsilon_{2}$-order ⋮ Nekrasov functions and the $\mathrm{SU}(2)$ Calogero-Moser system ⋮ The $\operatorname{SU}(r)_{2}$ string functions as $q$-diagrams ⋮ On the defect group of a 6D SCFT ⋮ Spectral networks and Fenchel-Nielsen coordinates ⋮ Gauge invariant computable quantities in timelike Liouville theory ⋮ Deformed Seiberg-Witten curves for ADE quivers ⋮ $N=1$ superconformal blocks with Ramond fields from AGT correspondence ⋮ $ \mathcal{N}=2 $ gauge theories on toric singularities, blow-up formulae and $W$-algebrae ⋮ Bootstrapping the superconformal index with surface defects ⋮ Exact results for perturbative partition functions of theories with $\mathrm{SU}(2| 4)$ symmetry ⋮ A 5d/2d/4d correspondence ⋮ The toroidal block and the genus expansion ⋮ $\mathcal{W}_3 $ irregular states and isolated $ \mathcal{N}=2 $ superconformal field theories ⋮ Superpolynomials for torus knots from evolution induced by cut-and-join operators ⋮ Bases in coset conformal field theory from AGT correspondence and Macdonald polynomials at the roots of unity ⋮ Deformed $ \mathcal{N}=2 $ theories, generalized recursion relations and S-duality ⋮ Genus one correction to Seiberg-Witten prepotential from $\beta$-deformed matrix model ⋮ On integrable structure and geometric transition in supersymmetric gauge theories ⋮ On S-duality of the superconformal index on Lens spaces and 2d TQFT ⋮ Chern-Simons theory and S-duality ⋮ Scheme dependence of instanton counting in ALE spaces ⋮ Chiral Liouville gravity ⋮ Exact results in $D = 2$ supersymmetric gauge theories ⋮ On three dimensional quiver gauge theories and integrability ⋮ BPS states in the duality web of the omega deformation ⋮ On the instanton $R$-matrix ⋮ Branching rules for quantum toroidal $\mathfrak{gl}_n$ ⋮ Quasimodular instanton partition function and the elliptic solution of Korteweg-de Vries equations ⋮ Free fermions, $W$-algebras, and isomonodromic deformations ⋮ Exts and the AGT relations ⋮ Quantum cohomology and quantum hydrodynamics from supersymmetric quiver gauge theories ⋮ $\mathcal{N} = 2$ gauge theories, instanton moduli spaces and geometric representation theory ⋮ Exact results for 't Hooft loops in gauge theories on $S^4$ ⋮ Line operator index on $S^{1}\times S^{3}$ ⋮ Quivers, YBE and 3-manifolds ⋮ Exceptional indices ⋮ M5-branes, toric diagrams and gauge theory duality ⋮ The ABCDEF's of matrix models for supersymmetric Chern-Simons theories ⋮ Line operators on $S^1\times\mathbb R^3$ and quantization of the Hitchin moduli space ⋮ Deformed planar topological open string amplitudes on Seiberg-Witten curve ⋮ Argyres-Douglas loci, singularity structures and wall-crossings in pure $ \mathcal{N} = 2 $ gauge theories with classical gauge groups ⋮ Generalized Whittaker states for instanton counting with fundamental hypermultiplets ⋮ Liouville theory, $ \mathcal{N} = 2 $ gauge theories and accessory parameters ⋮ Basic hypergeometry of supersymmetric dualities ⋮ On AGT description of $ \mathcal{N} = 2 $ SCFT with $N_{f } = 4$ ⋮ Recursive representation of the torus 1-point conformal block ⋮ Loop and surface operators in $ \mathcal{N} = 2 $ gauge theory and Liouville modular geometry ⋮ Five-dimensional AGT conjecture and the deformed Virasoro algebra ⋮ Gauge theory loop operators and Liouville theory ⋮ Matrix model conjecture for exact BS periods and Nekrasov functions ⋮ Penner type matrix model and Seiberg-Witten theory ⋮ On AGT conjecture ⋮ Gauge theory Wilson loops and conformal Toda field theory ⋮ Genus-one correction to asymptotically free Seiberg-Witten prepotential from Dijkgraaf-Vafa matrix model ⋮ Hitchin equation, singularity, and $N$ = 2 superconformal field theories ⋮ Correlators of supersymmetric Wilson loops at weak and strong coupling ⋮ S-duality and 2d topological QFT ⋮ $\mathcal{N} $ = 2 SCFTs: an M5-brane perspective ⋮ Matrix models for$\beta$-ensembles from Nekrasov partition functions ⋮ On the crossing relation in the presence of defects ⋮ Nekrasov functions and exact Bohr-Sommerfeld integrals ⋮ Gauge theories as matrix models ⋮ Topological expansion of the $\beta$-ensemble model and quantum algebraic geometry in the sectorwise approach ⋮ Resolvents and Seiberg-Witten representation for a Gaussian $\beta$-ensemble ⋮ Generalized Rogers Ramanujan identities motivated by AGT correspondence ⋮ Cherednik algebras, $W$-algebras and the equivariant cohomology of the moduli space of instantons on $\mathbb A^2$ ⋮ Curve counting, instantons and McKay correspondences ⋮ Gauge theories labelled by three-manifolds ⋮ Elliptic hypergeometry of supersymmetric dualities. II: Orthogonal groups, knots, and vortices ⋮ Three-dimensional extensions of the Alday-Gaiotto-Tachikawa relation ⋮ 6j symbols for the modular double, quantum hyperbolic geometry, and supersymmetric gauge theories ⋮ Wilson loop invariants from $W_{N}$ conformal blocks ⋮ Monodromic vs geodesic computation of Virasoro classical conformal blocks ⋮ AGT relations for abelian quiver gauge theories on ALE spaces ⋮ Whittaker vector of deformed Virasoro algebra and Macdonald symmetric functions ⋮ On a singular Fredholm-type integral equation arising in $\mathcal{N}=2$ super-Yang-Mills theories ⋮ Painlevé representation of Tracy-Widom$_\beta$ distribution for $\beta=6$ ⋮ Liouville quantum gravity on the Riemann sphere ⋮ Gauge theories on ALE space and super Liouville correlation functions ⋮ Spectral duality between Heisenberg chain and Gaudin model ⋮ Gauge theories and Macdonald polynomials ⋮ Instanton moduli spaces and bases in coset conformal field theory ⋮ The $\Omega $ deformed $B$-model for rigid $N=2$ theories ⋮ The gravity dual of supersymmetric gauge theories on a squashed three-sphere ⋮ Supersymmetric gauge theories on the five-sphere ⋮ Toda theory from six dimensions ⋮ Asymptotic M5-brane entropy from S-duality ⋮ Vertex operator algebras of Argyres-Douglas theories from M5-branes ⋮ On the large $R$-charge expansion in $ \mathcal{N}=2 $ superconformal field theories ⋮ Holographic duals of large-$c$ torus conformal blocks ⋮ Solving Heun's equation using conformal blocks ⋮ Splitting of surface defect partition functions and integrable systems ⋮ Chiral trace relations in $\mathcal{N}=2^*$ supersymmetric gauge theories ⋮ Discrete Painlevé system and the double scaling limit of the matrix model for irregular conformal block and gauge theory ⋮ A note on the algebraic engineering of 4D $\mathcal{N} = 2$ super Yang-Mills theories ⋮ Kac determinant and singular vector of the level $N$ representation of Ding-Iohara-Miki algebra ⋮ $q$-Virasoro modular triple ⋮ Plane partition realization of (web of) $ \mathcal{W} $-algebra minimal models ⋮ Deconstructing defects ⋮ Equivariant U($N$) Verlinde algebra from Bethe/gauge correspondence ⋮ $T[ \mathrm{SU} (N)$ duality webs: mirror symmetry, spectral duality and gauge/CFT correspondences] ⋮ BPS/CFT correspondence. IV: Sigma models and defects in gauge theory ⋮ Painlevé equations, topological type property and reconstruction by the topological recursion ⋮ New results in $\mathcal N=2$ theories from non-perturbative string ⋮ Refined geometric transition and $qq$-characters ⋮ Bands and gaps in Nekrasov partition function ⋮ Analyticity of Nekrasov partition functions ⋮ Fredholm determinant and Nekrasov sum representations of isomonodromic tau functions ⋮ Cluster integrable systems, $q$-Painlevé equations and their quantization ⋮ Quantizing higher-spin gravity in free-field variables ⋮ Chiral algebras, localization and surface defects ⋮ Green-Schwarz automorphisms and 6D SCFTs ⋮ Surface defects in E-string compactifications and the van Diejen model ⋮ Elliptic genus derivation of 4d holomorphic blocks ⋮ $(q, t)$-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces ⋮ Macdonald topological vertices and brane condensates ⋮ Trinion conformal blocks from topological strings ⋮ The Grassmannian VOA ⋮ Seiberg-Witten curves and double-elliptic integrable systems ⋮ Spherical Hecke algebra in the Nekrasov-Shatashvili limit ⋮ {$\Omega$}-deformation of B-twisted gauge theories and the 3d-3d correspondence ⋮ $tt^{*}$ equations, localization and exact chiral rings in $4d \mathcal{N} =2$ SCFTs ⋮ Quiver tails and $ \mathcal{N}=1 $ SCFTs from M5-branes ⋮ Resurgent analysis of localizable observables in supersymmetric gauge theories ⋮ On solutions of the Fuji-Suzuki-Tsuda system ⋮ Local conformal structure of Liouville quantum gravity ⋮ Quantum curves for Hitchin fibrations and the Eynard-Orantin theory ⋮ Holomorphicity and modularity in Seiberg-Witten theories with matter ⋮ Seiberg-Witten theory, matrix model and AGT relation ⋮ Refined cigar and {$\Omega$}-deformed conifold ⋮ Topological anti-topological fusion in four-dimensional superconformal field theories ⋮ Supersymmetric $\mathrm{AdS}_{3} \times S^{2}$ M-theory geometries with fluxes ⋮ The superconformal index of the $E_{6}$ SCFT ⋮ Isomonodromic tau-functions from Liouville conformal blocks ⋮ Infinite chiral symmetry in four dimensions ⋮ Duality of subregular $\mathcal{W} $-algebras and principal $\mathcal{W} $-superalgebras ⋮ Wilson-'t Hooft lines as transfer matrices ⋮ From VOAs to short star products in SCFT ⋮ Bootstrapping ADE M-strings ⋮ Higher rank FZZ-dualities ⋮ 4d F(4) gauged supergravity and black holes of class $\mathcal{F} $ ⋮ 4d $ \mathcal{N}=1/2 $ d Yang-Mills duality in holography ⋮ Kähler uniformization from holographic renormalization group flows of M5-branes ⋮ An elliptic vertex of Awata-Feigin-Shiraishi type for M-strings ⋮ Twist-field representations of W-algebras, exact conformal blocks and character identities ⋮ C-recursion for multi-point superconformal blocks. NS sector ⋮ Seiberg-Witten period relations in Omega background ⋮ From $\mathcal{N} = 4$ super-Yang-Mills on $\mathbb{R} \mathbb{P}^4$ to bosonic Yang-Mills on $\mathbb{R} \mathbb{P}^2$ ⋮ More on holographic correlators: twisted and dimensionally reduced structures ⋮ Vortex counting from field theory ⋮ A note on perturbation series in supersymmetric gauge theories ⋮ On non-stationary Lamé equation from WZW model and spin-1/2 XYZ chain ⋮ On gauge theory and topological string in Nekrasov-Shatashvili limit ⋮ Impure aspects of supersymmetric Wilson loops ⋮ $ \mathcal{N} = 2 $ superconformal blocks and instanton partition functions ⋮ Vertices, vortices \& interacting surface operators ⋮ The omega deformation from string and M-theory ⋮ Counting exceptional instantons ⋮ Comments on knotted 1/2 BPS Wilson loops ⋮ Large $N$ limit of $\beta$-ensembles and deformed Seiberg-Witten relations ⋮ Supersymmetry on curved spaces and holography ⋮ S-duality as a $\beta$-deformed Fourier transform ⋮ Seiberg-Witten theories on ellipsoids ⋮ Superconformal field theory and Jack superpolynomials ⋮ Compactification on the $\omega$-background and the AGT correspondence ⋮ $N=2$ generalized superconformal quiver gauge theory ⋮ Conformal field theory of Painlevé VI ⋮ Virasoro constraint for Nekrasov instanton partition function ⋮ BPS states in omega background and integrability ⋮ Matrix models for irregular conformal blocks and Argyres-Douglas theories ⋮ Conformal blocks of chiral fields in $ \mathcal{N}=2 $ SUSY CFT and affine laumon spaces ⋮ Superconformal index with duality domain wall ⋮ Surface operators in $ \mathcal{N} = 2$ 4d gauge theories ⋮ ABCD of beta ensembles and topological strings ⋮ Accessory parameters for Liouville theory on the torus ⋮ Liouville's imaginary shadow ⋮ Irregular singularities in Liouville theory and Argyres-Douglas type gauge theories ⋮ On 't Hooft defects, monopole bubbling and supersymmetric quantum mechanics ⋮ Correspondences among CFTs with different W-algebra symmetry ⋮ AGT basis in SCFT for c = 3/2 and Uglov polynomials ⋮ Correlator correspondences for subregular $\mathcal{W}$-algebras and principal $\mathcal{W}$-superalgebras ⋮ Fractional quiver W-algebras ⋮ Superconformal indices and instanton partition functions ⋮ Defects, nested instantons and comet-shaped quivers ⋮ Blowup equations for refined topological strings ⋮ Monopole bubbling via string theory ⋮ M5-branes on $S^2\times M_{4}$: Nahm's equations and 4d topological sigma-models ⋮ Factorization of differential expansion for antiparallel double-braid knots ⋮ Toric Calabi-Yau threefolds as quantum integrable systems. $\mathcal R$-matrix and $\mathcal{RTT}$ relations ⋮ $ \mathcal{W} $ -symmetry, topological vertex and affine Yangian ⋮ Holographic description of 2D conformal block in semi-classical limit ⋮ Chiral observables and S-duality in $\mathcal N=2^{\star} \mathrm{U}(N)$ gauge theories ⋮ VEV of Baxter's Q-operator in $N = 2$ gauge theory and the BPZ differential equation ⋮ K-decompositions and 3d gauge theories ⋮ Super-spectral curve of irregular conformal blocks ⋮ On new exact conformal blocks and Nekrasov functions ⋮ Exact partition functions for deformed $ \mathcal{N}=2 $ theories with $ {\mathcal{N}}_f=4 $ flavours ⋮ Wilson punctured network defects in 2D $q$-deformed Yang-Mills theory ⋮ 6d dual conformal symmetry and minimal volumes in AdS ⋮ 4d quantum geometry from 3d supersymmetric gauge theory and holomorphic block ⋮ Classical limit of irregular blocks and Mathieu functions ⋮ Surface operators and separation of variables ⋮ Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT ⋮ Correspondences between WZNW models and CFTs with $W$-algebra symmetry ⋮ Virasoro vacuum block at next-to-leading order in the heavy-light limit ⋮ Decomposing Nekrasov decomposition ⋮ Exact conformal blocks for the W-algebras, twist fields and isomonodromic deformations ⋮ Irregular conformal block, spectral curve and flow equations ⋮ BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and $qq$-characters ⋮ The $ \mathcal{N}=2 $ superconformal bootstrap ⋮ Deformed SW curve and the null vector decoupling equation in Toda field theory ⋮ S-duality, triangle groups and modular anomalies in $ \mathcal{N}=2 $ SQCD ⋮ M2-brane surface operators and gauge theory dualities in Toda ⋮ Hawking from Catalan ⋮ Conformal blocks beyond the semi-classical limit ⋮ The light asymptotic limit of conformal blocks in Toda field theory ⋮ Spectral duality in elliptic systems, six-dimensional gauge theories and topological strings ⋮ Higher-point conformal blocks and entanglement entropy in heavy states ⋮ Correlation functions with fusion-channel multiplicity in $ {\mathcal{W}}_3 $ Toda field theory ⋮ Quantization condition from exact WKB for difference equations ⋮ Two-dimensional SCFTs from D3-branes ⋮ On the large $\omega$-deformations in the Nekrasov-Shatashvili limit of $ \mathcal{N}={2}^{*} $ SYM ⋮ Exact partition functions for the $\omega$-deformed $\mathcal{N}={2}^{\ast} $ $SU(2)$ gauge theory ⋮ Explicit examples of DIM constraints for network matrix models ⋮ Exact WKB analysis of $ \mathcal{N} =2$ gauge theories ⋮ Toda 3-point functions from topological strings. II ⋮ RG domain wall for the general $ \widehat{su}(2) $ coset models ⋮ Second order RG flow in general $ \widehat{\mathrm{su}}(2) $ coset models ⋮ Symmetry enhancements via 5d instantons, $ q\mathcal{W} $-algebrae and $(1,0)$ superconformal index ⋮ Quiver W-algebras ⋮ Quiver elliptic W-algebras ⋮ Wall-crossing between stable and co-stable ADHM data ⋮ Teichmüller TQFT vs. Chern-Simons theory ⋮ 3d expansions of 5d instanton partition functions ⋮ Classical conformal blocks and accessory parameters from isomonodromic deformations ⋮ Conformal field theories and compact curves in moduli spaces ⋮ The DOZZ formula from the path integral ⋮ Orbifolds and exact solutions of strongly-coupled matrix models ⋮ Liouville conformal field theories in higher dimensions ⋮ Quantum integrability from non-simply laced quiver gauge theory ⋮ Quantum periods for $\mathcal{N} = 2 \operatorname{SU}(2)$ SQCD around the superconformal point ⋮ Exact quantization conditions, toric Calabi-Yau and non-perturbative topological string ⋮ An elliptic Virasoro symmetry in 6d ⋮ On Painlevé/gauge theory correspondence ⋮ $q$-Virasoro/$W$ algebra at root of unity and parafermions ⋮ Membrane quantum mechanics ⋮ Second level semi-degenerate fields in $ {\mathcal{W}}_3 $ Toda theory: matrix element and differential equation ⋮ Punctures for theories of class $ {\mathcal{S}}_{\Gamma} $ ⋮ Quantum spectral curve for $(q,t)$-matrix model ⋮ Modular and duality properties of surface operators in $ \mathcal{N}={2}^{\star} $ gauge theories ⋮ Intersecting surface defects and instanton partition functions ⋮ Framed sheaves on root stacks and supersymmetric gauge theories on ALE spaces ⋮ Supergravity one-loop corrections on $\mathrm{AdS}_{7}$ and $\mathrm{AdS}_{3}$, higher spins and AdS/CFT ⋮ Relaxed singular vectors, Jack symmetric functions and fractional level $\widehat{\mathfrak{sl}}(2)$ models ⋮ Colored HOMFLY polynomials as multiple sums over paths or standard Young tableaux ⋮ 2D CFT blocks for the 4D class $ {\mathcal{S}}_k $ theories ⋮ Quantum periods and prepotential in $ \mathcal{N}=2 \;$ SU(2) SQCD ⋮ SUSY monopole potentials in 2+1 dimensions ⋮ On the Kerr-AdS/CFT correspondence ⋮ Coupling of two conformal field theories and Nakajima-Yoshioka blow-up equations ⋮ RG-Whitham dynamics and complex Hamiltonian systems ⋮ The light asymptotic limit of conformal blocks in $ \mathcal{N}=1 $ super Liouville field theory ⋮ Refined toric branes, surface operators and factorization of generalized Macdonald polynomials ⋮ Recurrence relations for the $ {\mathcal{W}}_3 $ conformal blocks and $ \mathcal{N}=2 $ SYM partition functions ⋮ Complex Chern-Simons from M5-branes on the squashed three-sphere ⋮ Reflection states in Ding-Iohara-Miki algebra and brane-web for D-type quiver ⋮ Five-brane webs and highest weight representations ⋮ Exceptional $ \mathcal{N}=3 $ theories ⋮ Generalized Toda theory from six dimensions and the conifold ⋮ AGT/${\mathbb{Z}}_2$ ⋮ Central charges of 2d superconformal defects ⋮ New quantum toroidal algebras from 5D $\mathcal{N} = 1$ instantons on orbifolds ⋮ Type-B anomaly matching and the 6D (2,0) theory ⋮ Vector perturbations of Kerr-$\mathrm{AdS}_5$ and the Painlevé VI transcendent ⋮ On even spin ${\mathcal{W}}_{\infty }$ ⋮ Confluent conformal blocks of the second kind ⋮ Effective gravitational couplings of four-dimensional $\mathcal{N} = 2$ supersymmetric gauge theories ⋮ Weakly coupled conformal manifolds in $4d$ ⋮ Instantons, topological strings, and enumerative geometry ⋮ Towards the proof of AGT relations with the help of the generalized Jack polynomials ⋮ Tinkertoys for Gaiotto duality ⋮ F-theoretic vs microscopic description of a conformal $\mathcal{N} = 2$ SYM theory ⋮ AGT on the S-duality wall ⋮ Instanton partition functions in $\mathcal{N} = 2$ SU($N$) gauge theories with a general surface operator, and their $\mathcal{W}$-algebra duals ⋮ Elliptic recursion for 4-point superconformal blocks and bootstrap in $N = 1$ SLFT ⋮ Extended holomorphic anomaly in gauge theory ⋮ A direct proof of AGT conjecture at {$\beta$} = 1 ⋮ Boundary conditions in Toda theories and minimal models ⋮ Vortex counting and Lagrangian 3-manifolds ⋮ Method of generating q-expansion coefficients for conformal block and ${\mathcal N}=2$ Nekrasov function by $\beta $-deformed matrix model ⋮ Check of AGT relation for conformal blocks on sphere ⋮ Deformed prepotential, quantum integrable system and Liouville field theory ⋮ Conformal blocks and generalized Selberg integrals ⋮ Parafermionic polynomials, Selberg integrals and three-point correlation function in parafermionic Liouville field theory ⋮ Logarithmic potential $\beta $-ensembles and Feynman graphs ⋮ A note on Wilson-'t Hooft operators ⋮ Conformal blocks in Virasoro and W theories: Duality and the Calogero-Sutherland model ⋮ Ramond sector of super Liouville theory from instantons on an ALE space ⋮ Gauge theories on {$\Omega$}-backgrounds from non commutative Seiberg-Witten curves ⋮ On AGT conjecture for pure super Yang-Mills and W-algebra ⋮ SUSY gauge theories on squashed three-spheres ⋮ Whittaker vectors of the Virasoro algebra in terms of Jack symmetric polynomial ⋮ Relation between Nekrasov functions and Bohr-Sommerfeld periods in the pure $\mathrm{SU}(N)$ case ⋮ A finite analog of the AGT relation. I: Finite $W$-algebras and quasimaps' spaces ⋮ Instanton counting with a surface operator and the chain-saw quiver ⋮ Supergroup-extended super Liouville correspondence ⋮ Classical conformal blocks from TBA for the elliptic Calogero-Moser system ⋮ The virtue of defects in 4D gauge theories and 2D CFTs ⋮ Super Liouville conformal blocks from $ \mathcal{N} = 2 $ SU(2) quiver gauge theories ⋮ Generalized matrix models and AGT correspondence at all genera ⋮ Surface operator, bubbling Calabi-Yau and AGT relation ⋮ $ {\text{SL}}\left( {2,\mathbb{R}} \right) $ Chern-Simons, Liouville, and gauge theory on duality walls ⋮ Instantons on ALE spaces and super Liouville conformal field theories ⋮ Matrix models for random partitions ⋮ Norm of logarithmic primary of Virasoro algebra ⋮ On combinatorial expansion of the conformal blocks arising from AGT conjecture ⋮ Notes on SUSY gauge theories on three-sphere ⋮ Brezin-Gross-Witten model as ``pure gauge limit of Selberg integrals ⋮ From SO/Sp instantons to W-algebra blocks ⋮ On W-algebras and the symmetries of defects of 6d $\mathcal{N} = \left( {2,0} \right)$ theory ⋮ Proving AGT conjecture as HS duality: Extension to five dimensions ⋮ Baxter's T-Q equation, $\mathrm{SU}(N)/\mathrm{SU}(2)^{N-3}$ correspondence and {$\Omega$}-deformed Seiberg-Witten prepotential ⋮ Vortices on orbifolds ⋮ Instantons and 2d superconformal field theory ⋮ The Liouville side of the vortex ⋮ On topological field theory representation of higher analogs of classical special functions ⋮ Dimer models, integrable systems and quantum Teichmüller space ⋮ A new 2d/4d duality via integrability ⋮ Non-perturbative topological strings and conformal blocks ⋮ Matrix model from $ \mathcal{N} = 2 $ orbifold partition function ⋮ Painlevé functions and conformal blocks ⋮ 3d and 5d gauge theory partition functions as $q$-deformed CFT correlators ⋮ Towards a 4d/2d correspondence for Sicilian quivers ⋮ Quantization of integrable systems and a $2d/4d$ duality ⋮ A search for $\mathrm{AdS}_{5} {\times} S^{2}$ IIB supergravity solutions dual to $ \mathcal{N} = 2 $ SCFTs ⋮ Chiral rings for surface operators in 4d and 5d SQCD ⋮ Vertex algebras at the corner ⋮ Bilinear equations on Painlevé $\tau$ functions from CFT ⋮ Spiked instantons from intersecting D-branes ⋮ Chiral trace relations in $\Omega$-deformed $\mathcal{N}=2 $ theories ⋮ Little string origin of surface defects ⋮ Quantum geometry of resurgent perturbative/nonperturbative relations ⋮ Four-dimensional $\mathcal{N} =2 $ supersymmetric theory with boundary as a two-dimensional complex Toda theory ⋮ Refined BPS invariants of 6d SCFTs from anomalies and modularity ⋮ Exact deconstruction of the 6D (2,0) theory ⋮ Spectral curves of $\mathcal{N} = 1$ theories of class ${\mathcal{S}}_k $ ⋮ Irregular conformal states and spectral curve: irregular matrix model approach ⋮ Fusion transformations in Liouville theory ⋮ Quantum holonomies from spectral networks and framed BPS states ⋮ Nekrasov and Argyres-Douglas theories in spherical Hecke algebra representation ⋮ On AGT relations with surface operator insertion and a stationary limit of beta-ensembles ⋮ Seiberg-Witten curve via generalized matrix model ⋮ Affine $sl(N)$ conformal blocks from ${\mathcal N} = 2$ $SU(N)$ gauge theories ⋮ The volume conjecture, perturbative knot invariants, and recursion relations for topological strings ⋮ AGT conjecture and integrable structure of conformal field theory for $c=1$ ⋮ Affine $SL(2)$ conformal blocks from 4d gauge theories ⋮ (de)tails of Toda CFT ⋮ Deforming SW curve ⋮ Tau-functions for quiver gauge theories ⋮ M-theoretic derivations of 4d-2d dualities: from a geometric Langlands duality for surfaces, to the AGT correspondence, to integrable systems ⋮ Coset conformal field theory and instanton counting on $\mathbb{C}^{2}/\mathbb{Z}_{p}$ ⋮ Quarter-BPS $\mathrm{AdS}_5$ solutions in M-theory with a $T^2$ bundle over a Riemann surface ⋮ On the integrability of four dimensional $ \mathcal{N}=2 $ gauge theories in the omega background ⋮ Hyperbolic deformation of the strip-equation and the accessory parameters for the torus ⋮ Exact results in $ \mathcal{N}=2 $ gauge theories ⋮ AGT relation in the light asymptotic limit ⋮ Extended supersymmetry on curved spaces ⋮ $\mathcal{N} =1$ geometries via M-theory ⋮ Transformations of spherical blocks ⋮ Surface defects, the superconformal index and $q$-deformed Yang-Mills ⋮ Modular anomaly equation, heat kernel and S-duality in $ \mathcal{N}=2 $ theories ⋮ On spectrum of ILW hierarchy in conformal field theory ⋮ Spectral dualities in XXZ spin chains and five dimensional gauge theories ⋮ Painlevé VI connection problem and monodromy of $c$\ =\ 1 conformal blocks ⋮ General Argyres-Douglas theory ⋮ Matching branches of a nonperturbative conformal block at its singularity divisor ⋮ On the renormalization group flow in two dimensional superconformal models ⋮ BPS states, crystals, and matrices ⋮ Quantisation of super Teichmüller theory ⋮ Check-operators and quantum spectral curves ⋮ Gauge theories on compact toric surfaces, conformal field theories and equivariant Donaldson invariants ⋮ Seiberg-Witten theory as a Fermi gas ⋮ $q$-Virasoro modular double and 3d partition functions ⋮ Comments on fusion matrix in $\mathbf{N} = 1$ super Liouville field theory ⋮ $\mathcal{N} = 2^{\star}$ from topological amplitudes in string theory ⋮ Holomorphic anomaly in gauge theory on ALE space ⋮ Fiber-base duality and global symmetry enhancement ⋮ Holography of 3d-3d correspondence at large N ⋮ 3d mirror symmetry as a canonical transformation ⋮ $\mathcal{W}$ symmetry in six dimensions ⋮ The superconformal index of the $(2,0)$ theory with defects ⋮ Defects and quantum Seiberg-Witten geometry ⋮ Generalized Macdonald polynomials, spectral duality for conformal blocks and AGT correspondence in five dimensions ⋮ Toda 3-point functions from topological strings ⋮ A surprising relation for the effective coupling constants of $N = 2$ super Yang-Mills theories ⋮ Electric-magnetic duality of abelian gauge theory on the four-torus, from the fivebrane on $T^2\times T^4$, via their partition functions ⋮ On skein relations in class S theories ⋮ $ \mathcal{N}=2 $ supersymmetric gauge theories on $S^{2} \times S^{2}$ and Liouville gravity ⋮ $ \mathcal{N}=1 $ theories of class $ {\mathcal{S}}_k $ ⋮ High-temperature expansion of supersymmetric partition functions ⋮ A topologically twisted index for three-dimensional supersymmetric theories ⋮ From topological strings to minimal models ⋮ On the energy spectrum of Yang-Mills instantons over asymptotically locally flat spaces ⋮ Deformed Virasoro algebras from elliptic quantum algebras ⋮ Quantum geometry and quiver gauge theories ⋮ BPS/CFT correspondence. III: Gauge origami partition function and $qq$-characters ⋮ Quantum Hitchin systems via $\beta$-deformed matrix models ⋮ An $ \mathcal{N}=1 $ 3d-3d correspondence ⋮ A freely generated ring for $\mathcal{N}=1$ models in class $ {\mathcal{S}}_k $ ⋮ Bosonic higher spin gravity in any dimension with dynamical two-form ⋮ Fiber-base duality from the algebraic perspective ⋮ Higgs and Coulomb branches from vertex operator algebras ⋮ New vortex-string worldsheet theories from supersymmetric localization ⋮ On the correspondence between surface operators in Argyres-Douglas theories and modules of chiral algebra ⋮ Holographic entanglement entropy from probe M-theory branes ⋮ Recursive representations of arbitrary Virasoro conformal blocks ⋮ Holographic aspects of four dimensional $\mathcal{N} = 2$ SCFTs and their marginal deformations ⋮ 2d-4d connection between $q$-Virasoro/$W$ block at root of unity limit and instanton partition function on ALE space ⋮ Notes on Mayer expansions and matrix models ⋮ Local logarithmic correlators as limits of Coulomb Gas integrals ⋮ Symmetries of quantum Lax equations for the Painlevé equations ⋮ The Hilbert series of the one instanton moduli space ⋮ TBA for non-perturbative moduli spaces ⋮ Proving the AGT relation for $N_{f} = 0, 1, 2$ antifundamentals ⋮ Abelian dualities of $\mathcal{N} = (0, 4)$ boundary conditions ⋮ Combinatorial expansions of conformal blocks ⋮ Calculations in conformal theory needed for verifying the Alday-Gaiotto-Tachikawa hypothesis ⋮ Cut-and-join operators and Macdonald polynomials from the 3-Schur functions ⋮ Cluster integrable systems and spin chains ⋮ Topological AdS/CFT and the $\Omega$ deformation ⋮ Gluing two affine Yangians of $\mathfrak{g} \mathfrak{l}_1$ ⋮ IIB flux non-commutativity and the global structure of field theories ⋮ 't Hooft defects and wall crossing in SQM ⋮ M5 branes and theta functions ⋮ Discrete Painlevé equation, Miwa variables and string equation in 5D matrix models ⋮ The resurgence of instantons: multi-cut Stokes phases and the Painlevé II equation ⋮ Singular vectors of the Ding-Iohara-Miki algebra ⋮ Vortex partition functions, wall crossing and equivariant Gromov-Witten invariants ⋮ Complex Chern-Simons theory at level $k$ via the 3d-3d correspondence ⋮ Duality walls in the 4d $\mathcal{N} = 2$$\mathrm{SU}(N)$ gauge theory with $2N$ flavours ⋮ From $3d$ dualities to $2d$ free field correlators and back ⋮ Instantons from blow-up ⋮ Wall-crossing and operator ordering for 't Hooft operators in $\mathcal{N} = 2$ gauge theories ⋮ Higher-rank isomonodromic deformations and $W$-algebras ⋮ Universal correlation functions in rank 1 SCFTs ⋮ Instanton R-matrix and $\mathcal{W}$-symmetry ⋮ Exact SUSY Wilson loops on $S^3$ from $q$-Virasoro constraints ⋮ The matrix-extended ${\mathcal{W}}_{1+\infty}$ algebra ⋮ $t,q$-deformed $Q$-systems, DAHA and quantum toroidal algebras via generalized Macdonald operators ⋮ $3d$ field theory, plane partitions and triple Macdonald polynomials ⋮ Lifshitz scaling, microstate counting from number theory and black hole entropy ⋮ Quantum anomalies in $ A_r^{(1)} $ Toda theories with defects ⋮ Tensor product weight modules of Schrödinger-Virasoro algebras ⋮ Vertex operator algebras and 3d $ \mathcal{N} = 4 $ gauge theories ⋮ Wilson surface central charge from holographic entanglement entropy ⋮ Kerr-De Sitter quasinormal modes via accessory parameter expansion ⋮ On monopole bubbling contributions to 't Hooft loops ⋮ $ \mathcal{N} = 2 $ gauge theories on unoriented/open four-manifolds and their AGT counterparts ⋮ Pentagon identities arising in supersymmetric gauge theory computations ⋮ $W$-algebras as coset vertex algebras ⋮ Combinatorial expressions for the tau functions of $q$-Painlevé V and III equations ⋮ Web construction of ABCDEFG and affine quiver gauge theories ⋮ An infrared bootstrap of the Schur index with surface defects ⋮ Argyres-Douglas theories and Liouville irregular states ⋮ F-theory, Seiberg-Witten curves and $\mathcal{N} = {2}$ dualities ⋮ $\beta$-deformed matrix model and Nekrasov partition function ⋮ BPS dyons and Hesse flow ⋮ Parafermionic Liouville field theory and instantons on ALE spaces ⋮ Wild quiver gauge theories ⋮ On the six-dimensional origin of the AGT correspondence ⋮ The large central charge limit of conformal blocks ⋮ Loop equations and topological recursion for the arbitrary-$\beta$ two-matrix model ⋮ The ABCDEFG of instantons and W-algebras ⋮ Quantum algebraic approach to refined topological vertex ⋮ On the instantons and the hypermultiplet mass of $\mathcal{N} = {{2}^{\ast}}$ super Yang-Mills on $S^{4}$ ⋮ Omega-deformed Seiberg-Witten effective action from the M$_5$-brane ⋮ Finite $\varepsilon_2$-corrections to the $\mathcal{N} = 2 \mathrm{SYM}$ prepotential ⋮ Superconformal minimal models and admissible Jack polynomials ⋮ Surface defects in gauge theory and KZ equation ⋮ Black hole quasinormal modes and Seiberg-Witten theory ⋮ Correspondences of categories for subregular $\mathcal{W}$-algebras and principal $\mathcal{W}$-superalgebras ⋮ Quantum spectral problems and isomonodromic deformations ⋮ Supersymmetric Wilson loops, instantons, and deformed $\mathcal{W}$-algebras ⋮ Tetrahedron instantons ⋮ Toda conformal blocks, quantum groups, and flat connections ⋮ Stacky dualities for the moduli of Higgs bundles ⋮ Screening operators and parabolic inductions for affine $\mathcal{W}$-algebras ⋮ Extensions of the asymptotic symmetry algebra of general relativity ⋮ On extensions of $\mathfrak{gl}\widehat{\left(m \vert n \right)}$ Kac-Moody algebras and Calabi-Yau singularities ⋮ Higher-form symmetries, Bethe vacua, and the 3d-3d correspondence ⋮ Semi-classical Virasoro blocks: proof of exponentiation ⋮ Unitary matrix with a Penner-like potential also yields $N_f = 2$ ⋮ On quiver W-algebras and defects from gauge origami ⋮ Twisting with a flip (The art of pestunization) ⋮ Cohomological Hall algebras, vertex algebras and instantons ⋮ Mirror symmetry and line operators ⋮ Integrating over quiver variety and BPS/CFT correspondence ⋮ Integrability and cycles of deformed $\mathcal{N} = 2$ gauge theory ⋮ 2-parameter $\tau$-function for the first Painlevé equation: topological recursion and direct monodromy problem via exact WKB analysis ⋮ $\mathcal{N} = 2^*$ gauge theory, free fermions on the torus and Painlevé VI ⋮ Universal 3d Cardy block and black hole entropy ⋮ Toward the pole ⋮ Generalized Macdonald functions on Fock tensor spaces and duality formula for changing preferred direction ⋮ Exact WKB and abelianization for the $T_3$ equation ⋮ Non-stationary Ruijsenaars functions for $\kappa = t^{-1/N}$ and intertwining operators of Ding-Iohara-Miki algebra ⋮ The Virasoro fusion kernel and Ruijsenaars' hypergeometric function ⋮ Taming defects in $\mathcal{N} = 4$ super-Yang-Mills ⋮ Spectra of elliptic potentials and supersymmetric gauge theories ⋮ Elliptic lift of the Shiraishi function as a non-stationary double-elliptic function ⋮ $\widehat{\mathfrak{sl}}(n)_N$ WZW conformal blocks from $SU(N)$ instanton partition functions on $\mathbb{C}^2/\mathbb{Z}_N$ ⋮ Virasoro blocks at large exchange dimension ⋮ Non-unitary TQFTs from 3D $\mathcal{N} = 4$ rank 0 SCFTs ⋮ 4d Chern-Simons theory as a 3d Toda theory, and a 3d-2d correspondence ⋮ Instanton counting and O-vertex ⋮ Characters, coadjoint orbits and Duistermaat-Heckman integrals ⋮ Virasoro constraints revisited ⋮ AFLT-type Selberg integrals ⋮ The matrix model version of AGT conjecture and CIV-DV prepotential ⋮ A \& B model approaches to surface operators and Toda thoeries ⋮ The omega deformation, branes, integrability and Liouville theory ⋮ Disk one-point function for a family of non-rational conformal theories ⋮ Uniformization, Calogero-Moser/Heun duality and Sutherland/bubbling pants ⋮ Relating gauge theories via Gauge/Bethe correspondence ⋮ Integrable QFT and Longo-Witten endomorphisms ⋮ M-strings ⋮ Partition functions of $\mathcal N=(2,2)$ gauge theories on $S^2$ and vortices ⋮ 't Hooft operators in gauge theory from Toda CFT ⋮ The exact 8d chiral ring from 4d recursion relations ⋮ Notes on 3-point functions of $A_{N-1}$ Toda theory and AGT-W relation for $\operatorname{SU}(N)$ quiver ⋮ Selberg integral and $\mathrm{SU}(N)$ AGT conjecture ⋮ Analytic continuation of Liouville theory ⋮ Integrable structure, W-symmetry and AGT relation ⋮ Darboux coordinates, Yang-Yang functional, and gauge theory ⋮ Dual infrared limits of 6d $\mathcal{N} = (2, 0)$ theory ⋮ Macmahon KZ equation for Ding-Iohara-Miki algebra ⋮ Comments on chiral algebras and $\Omega$-deformations ⋮ $q$-deformation of corner vertex operator algebras by Miura transformation ⋮ Argyres-Douglas theories, S-duality and AGT correspondence ⋮ New modular invariants in $\mathcal{N} = 4$ super-Yang-Mills theory ⋮ Extremal correlators and random matrix theory ⋮ ABCD of 't Hooft operators ⋮ S-duality and correlation functions at large R-charge ⋮ On $q$-isomonodromic deformations and $q$-Nekrasov functions ⋮ Blowup relations on $\mathbb{C}^2/\mathbb{Z}_2$ from Nakajima-Yoshioka blowup relations ⋮ The ABCDEFG of little strings ⋮ Gauge theories on compact toric manifolds ⋮ Circular quiver gauge theories, isomonodromic deformations and $W_N$ fermions on the torus ⋮ Dessins d'enfants, Seiberg-Witten curves and conformal blocks ⋮ Intersecting surface defects and 3d superconformal indices ⋮ Remarks on holographic models of the Kerr-$ \mathrm{AdS}_5$ geometry ⋮ Hilbert schemes of nonreduced divisors in Calabi-Yau threefolds and $W$-algebras ⋮ Accessory parameters in confluent Heun equations and classical irregular conformal blocks ⋮ QNMs of branes, BHs and fuzzballs from quantum SW geometries ⋮ 3D fermion representation of affine Yangian ⋮ Coproduct for affine Yangians and parabolic induction for rectangular $W$-algebras ⋮ Mixed network calculus ⋮ $\mathfrak{gl}_N$ Higgsed networks ⋮ Quasi-Hopf twist and elliptic Nekrasov factor ⋮ Correlator correspondences for Gaiotto-Rapčák dualities and first order formulation of coset models ⋮ A geometric recipe for twisted superpotentials ⋮ The colored Jones polynomials as vortex partition functions ⋮ Weyl anomalies of four dimensional conformal boundaries and defects ⋮ More on the SW-QNM correspondence ⋮ Trialities of orthosymplectic $\mathcal{W} $-algebras ⋮ Quasi-normal modes for the D3-branes and exact WKB analysis ⋮ Exact WKB and the quantum Seiberg-Witten curve for 4d $N = 2$ pure SU(3) Yang-Mills. Abelianization ⋮ Virasoro constraint for Uglov matrix model ⋮ Classical conformal blocks, Coulomb gas integrals and Richardson-Gaudin models ⋮ Dualities in quantum integrable many-body systems and integrable probabilities. I. ⋮ Jack polynomials and affine Yangian ⋮ Quiver Yangian and supersymmetric quantum mechanics ⋮ A note on quiver quantum toroidal algebra ⋮ Shifted quiver quantum toroidal algebra and subcrystal representations ⋮ M2-branes and ${\mathfrak{q}}$-Painlevé equations ⋮ Crystal melting, BPS quivers and plethystics ⋮ OPE coefficients in Argyres-Douglas theories ⋮ Constraints in the BV formalism: six-dimensional supersymmetry and its twists ⋮ Singular modules for affine Lie algebras, and applications to irregular WZNW conformal blocks ⋮ Fivebranes and 4-Manifolds ⋮ (β-deformed) Hurwitz–Kontsevich model and affine Yangian of gl(1) ⋮ Painlevé/CFT correspondence on a torus ⋮ A path model for Whittaker vectors ⋮ A Macdonald refined topological vertex ⋮ Exact thermal correlators of holographic \textit{CFT}s ⋮ Quiver Yangians and -algebras for generalized conifolds ⋮ A New Treatment for Some Periodic Schrödinger Operators II: The Wave Function ⋮ Quantum curves from refined topological recursion: the genus 0 case ⋮ On irregular states and Argyres-Douglas theories ⋮ A Rutherford-like formula for scattering off Kerr-Newman BHs and subleading corrections ⋮ More on affine Dynkin quiver Yangians ⋮ Partition functions of non-Lagrangian theories from the holomorphic Anomaly ⋮ Effective gravitational couplings of Kaluza-Klein gauge theories ⋮ Non-stationary difference equation and affine Laumon space: quantization of discrete Painlevé equation ⋮ The cohomological Hall algebra of a surface and factorization cohomology ⋮ Little string instanton partition functions and scalar propagators ⋮ 2-charge circular fuzz-balls and their perturbations ⋮ The black hole behind the cut ⋮ Generalized devil's staircase and RG flows ⋮ 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 ⋮ Crystallization of deformed Virasoro algebra, Ding-Iohara-Miki algebra, and 5D AGT correspondence ⋮ Double quiver gauge theory and BPS/CFT correspondence ⋮ Twisted index on hyperbolic four-manifolds ⋮ On the status of DELL systems ⋮ On the convergence of Nekrasov functions ⋮ Subregular W-algebras of type A ⋮ Affine Laumon spaces and iterated $\mathcal{W}$-algebras ⋮ Holographic thermal correlators for hyperbolic CFTs ⋮ Instantons on Young diagrams with matters ⋮ Bootstrapping closed string field theory ⋮ Anyonic defect branes and conformal blocks in twisted equivariant differential (TED) K-theory ⋮ Seiberg-Witten geometry of four-dimensional $\mathcal{N}=2$ quiver gauge theories ⋮ A note on rank 5/2 Liouville irregular block, Painlevé I and the $\mathcal{H}_0$ Argyres-Douglas theory ⋮ SymTFTs and duality defects from 6d SCFTs on 4-manifolds ⋮ Absorption cross section in gravity’s rainbow from confluent Heun equation ⋮ Orthosymplectic superinstanton counting and brane dynamics ⋮ Blowups in BPS/CFT correspondence, and Painlevé VI ⋮ Whittaker vectors for $\mathcal{W}$-algebras from topological recursion ⋮ A thermal product formula ⋮ The Higgs branch of heterotic ALE instantons ⋮ On the stability and deformability of top stars ⋮ More largeNlimits of 3d gauge theories ⋮ Elliptic algebra, Frenkel–Kac construction and root of unity limit ⋮ On the solution of the Liouville equation ⋮ On spectrum of ILW hierarchy in conformal field theory II: coset CFT's ⋮ Double quantization of Seiberg–Witten geometry and W-algebras ⋮ On dimensional transmutation in 1 + 1D quantum hydrodynamics ⋮ ${\cal N}=2$ N = 2 gauge theories: Congruence subgroups, coset graphs, and modular surfaces ⋮ Seiberg-Witten equations and non-commutative spectral curves in Liouville theory ⋮ Magnificent four ⋮ Hidden structures of knot invariants ⋮ Condensates and instanton - torus knot duality. Hidden Physics at UV scale ⋮ Introduction ⋮ VOA[M4] ⋮ Wilson loops and chiral correlators on squashed spheres ⋮ Wilson loops and chiral correlators on squashed spheres ⋮ Combinatorial approach to Mathieu and Lamé equations ⋮ Five-dimensional SU(2) AGT conjecture and recursive formula of deformed Gaiotto state ⋮ Urod algebras and Translation of W-algebras ⋮ The uses of the refined matrix model recursion ⋮ Coloured refined topological vertices and parafermion conformal field theories ⋮ A slow review of the AGT correspondence ⋮ Resurgence, Painlevé equations and conformal blocks ⋮ The Pollica perspective on the (super)-conformal world ⋮ Observations on BPS observables in 6D ⋮ Intersecting defects and supergroup gauge theory ⋮ Perturbative connection formulas for Heun equations ⋮ Zeros of the isomonodromic tau functions in constructive conformal mapping of polycircular arc domains: the n-vertex case ⋮ WKB method and quantum periods beyond genus one ⋮ String theory and math: Why this marriage may last. Mathematics and dualities of quantum physics ⋮ Yang–Baxter algebra and MacMahon representation ⋮ Classical Virasoro irregular conformal block ⋮ Classical conformal blocks via AdS/CFT correspondence ⋮ Dessins d'enfants in $ \mathcal{N}=2 $ generalised quiver theories ⋮ Virasoro conformal blocks in closed form ⋮ Pure $ \mathcal{N}=2 $ super Yang-Mills and exact WKB ⋮ Classical Virasoro irregular conformal block. II ⋮ The condensate from torus knots ⋮ Exploring $\mathcal W_{\infty}$ in the quadratic basis ⋮ Exact results for boundaries and domain walls in 2d supersymmetric theories ⋮ Isomonodromic $\tau$-functions and $W_{N}$ conformal blocks ⋮ AGT, $N$-Burge partitions and $ {\mathcal{W}}_N $ minimal models ⋮ Modular anomaly equations and S-duality in $ \mathcal{N}=2 $ conformal SQCD ⋮ On a canonical quantization of 3D anti de Sitter pure gravity ⋮ Discrete Painlevé system for the partition function of N _f = 2 SU(2) supersymmetric gauge theory and its double scaling limit ⋮ Line operators in theories of class $ \mathcal{S} $, quantized moduli space of flat connections, and Toda field theory ⋮ Ellipsoid partition function from Seiberg-Witten monopoles ⋮ Universal consistent truncation for 6d/7d gauge/gravity duals ⋮ Kerr scattering coefficients via isomonodromy ⋮ Construction of 4d SYM compactified on open Riemann surfaces by the superfield formalism ⋮ Large $N$ matrix hyperspheres and the gauge-gravity correspondence ⋮ Semiclassical Virasoro blocks from $\mathrm{AdS}_{3}$ gravity ⋮ On some 3-point functions in the $W_4$ CFT and related braiding matrix ⋮ Partially twisted superconformal M5 brane in R-symmetry gauge field backgrounds ⋮ Angular momentum and gravimagnetization of the ${\mathcal N=2}$ supersymmetric vacuum ⋮ Quiver ${\text{W}}_{{\boldsymbol{{\epsilon}}}_{\mathbf{1}},{\boldsymbol{{\epsilon}}}_{\mathbf{2}}}$ algebras of 4D $\boldsymbol{\mathcal{N}}\mathbf{=}\mathbf{2}$ gauge theories ⋮ 4D $\boldsymbol{\mathcal{N}}\mathbf{=}$ 2 SCFTs and spin chains ⋮ Instanton counting in class Sk ⋮ Irregular conformal blocks, with an application to the fifth and fourth Painlevé equations ⋮ ϵ-CORRECTED SEIBERG–WITTEN PREPOTENTIAL OBTAINED FROM HALF-GENUS EXPANSION IN β-DEFORMED MATRIX MODEL ⋮ TOWARDS A PROOF OF AGT CONJECTURE BY METHODS OF MATRIX MODELS ⋮ TOWARDS THE LOCALIZATION OF SUSY GAUGE THEORY ON A CURVED SPACE ⋮ S-duality wall of SQCD from Toda braiding ⋮ Virasoro blocks and quasimodular forms ⋮ Modular invariance in superstring theory from $\mathcal{N} = 4$ super-Yang-Mills ⋮ Random boundary geometry and gravity dual of $T\overline{T}$ deformation ⋮ Riemann-Hilbert correspondence and blown up surface defects ⋮ Liouville reflection operator, affine Yangian and Bethe ansatz ⋮ On colored HOMFLY polynomials for twist knots ⋮ Super topological recursion and Gaiotto vectors for superconformal blocks ⋮ Dynamical centers for the elliptic quantum algebra $ \newcommand{\elpb}[1{{{\mathcal{B}}_{q,\lambda}(\widehat{gl}_{#1})_c}} \newcommand{\e}{{\rm e}} \elpb{2}$] ⋮ A note on quiver Yangians and $\mathcal{R}$-matrices ⋮ Celestial Liouville theory for Yang-Mills amplitudes ⋮ Symmetric functions and 3D fermion representation of $W_{1+\infty}$ algebra ⋮ 2D quantum gravity partition function on the fluctuating sphere ⋮ Effective gravitational couplings of higher-rank supersymmetric gauge theories ⋮ The ``Null-A superintegrability for monomial matrix models ⋮ Introduction to localization in quantum field theory ⋮ Supersymmetric localization in two dimensions ⋮ Perturbative and nonperturbative aspects of complex Chern–Simons theory ⋮ ${{{\mathcal N}}=2}$ SUSY gauge theories on S⁴ ⋮ A brief review of the 2d/4d correspondences ⋮ Holomorphic blocks and the 5d AGT correspondence ⋮ Indices for 6 dimensional superconformal field theories ⋮ Topological string amplitudes and Seiberg-Witten prepotentials from the counting of dimers in transverse flux ⋮ The $R$-matrix of the quantum toroidal algebra ⋮ 3-Jack polynomials and Yang-Baxter equation ⋮ HYPERBOLIC 3-MANIFOLDS AND CLUSTER ALGEBRAS ⋮ AGT and the Segal-Sugawara construction ⋮ Isomonodromic tau functions on a torus as Fredholm determinants, and charged partitions ⋮ More on Seiberg-Witten theory and monstrous moonshine: a new simple method of calculating the prepotential ⋮ CFT description of BH's and ECO's: QNMs, superradiance, echoes and tidal responses ⋮ Elliptic modular double and 4d partition functions ⋮ 5d AGT correspondence of supergroup gauge theories from quantum toroidal $\mathfrak{gl}_1$ ⋮ On the Nekrasov partition function of gauged Argyres-Douglas theories ⋮ Bootstrapping $\mathcal{N} = 4$ super-Yang-Mills on the conformal manifold ⋮ Bootstrapping 4d $\mathcal{N} = 2$ gauge theories: the case of SQCD ⋮ Irregular Liouville correlators and connection formulae for Heun functions ⋮ Elliptic quantum toroidal algebra $U_{q,t,p}(\mathfrak{gl}_{1,tor})$ and affine quiver gauge theories ⋮ Bäcklund transformation of Painlevé III(D₈)τfunction ⋮ Supersymmetric field theories and geometric Langlands: The other side of the coin ⋮ Pure 𝑆𝑈(2) gauge theory partition function and generalized Bessel kernel ⋮ An elliptic topological vertex ⋮ Quantum $q$-Langlands Correspondence ⋮ Algebraic structures on the moduli spaces in gauge theories ⋮ Accessory parameters in conformal mapping: exploiting the isomonodromic tau function for Painlevé VI ⋮ ON THE DESCRIPTION OF SURFACE OPERATORS IN ${\mathcal N} = 2^*$ SYM ⋮ SEIBERG–WITTEN PREPOTENTIAL FROM WZNW CONFORMAL BLOCK: LANGLANDS DUALITY AND SELBERG TRACE FORMULA ⋮ SOME REMARKS ON D-BRANES AND DEFECTS IN LIOUVILLE AND TODA FIELD THEORIES ⋮ The Toda system and solution to the N = 2 SUSY Yang–Mills theory ⋮ Irregular conformal blocks and connection formulae for Painlevé V functions ⋮ Exact Results on $${\mathcal N}=2$$ Supersymmetric Gauge Theories ⋮ The Superconformal Index of Theories of Class $$\mathcal {S}$$ ⋮ 3d Superconformal Theories from Three-Manifolds ⋮ Supersymmetric Gauge Theories, Quantization of $${\mathcal M}_\mathrm{flat}$$ , and Conformal Field Theory ⋮ Gauge/Vortex Duality and AGT ⋮ B-Model Approach to Instanton Counting ⋮ Universal two-parameter 𝒲_∞-algebra and vertex algebras of type 𝒲(2, 3, …, N) ⋮ Non-perturbative studies of N=2 conformal quiver gauge theories ⋮ Bootstrap methods in CFT ⋮ Higher-dimensional gauge theories from string theory ⋮ On elliptic algebras and large-n supersymmetric gauge theories ⋮ Derived representation schemes and supersymmetric gauge theory ⋮ W-Algebras via Lax Type Operators ⋮ Whittaker pairs for the Virasoro algebra and the Gaiotto-Bonelli-Maruyoshi-Tanzini states ⋮ DEFORMED SUPERSYMMETRIC GAUGE THEORIES FROM THE FLUXTRAP BACKGROUND ⋮ Confinement and Mayer cluster expansions

Cites Work