Hitchin systems, N=2 gauge theories and W-gravity

Abstract

We propose some arguments supporting an M-theory derivation of the duality recently discovered by Alday, Gaiotto and Tachikawa between two-dimensional conformal field theories and N=2 superconformal gauge theories in four dimensions. We find that A_{N-1} Toda field theory is the simplest two-dimensional conformal field theory quantizing the moduli of N M5-branes wrapped on a Riemann surface. This leads us to identify chiral operators of the N=2 gauge theories with W-algebra currents. As a check of this correspondence we study some relevant OPE's obtaining that Nekrasov's partition function satisfies W-geometry constraints.

1 + 9 pages; v.2 refs and comments added; v3 version to appear on PLB

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Cited by in corpus (94)

• Nekrasov Functions and Exact Bohr-Sommerfeld Integrals
• S-duality and 2d Topological QFT
• Four-Dimensional SCFTs from M5-Branes
• Five-dimensional AGT Conjecture and the Deformed Virasoro Algebra
• SL(2,R) Chern-Simons, Liouville, and Gauge Theory on Duality Walls
• Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions
• Wild Quiver Gauge Theories
• Para-Liouville/Toda central charges from M5-branes
• Conformal blocks as Dotsenko-Fateev Integral Discriminants
• The Quiver Matrix Model and 2d-4d Conformal Connection
• Deformed Prepotential, Quantum Integrable System and Liouville Field Theory
• Nekrasov Functions from Exact BS Periods: the Case of SU(N)
• Proving AGT conjecture as HS duality: extension to five dimensions
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• Method of Generating q-Expansion Coefficients for Conformal Block and N=2 Nekrasov Function by beta-Deformed Matrix Model
• Non-Lagrangian Theories from Brane Junctions
• Instanton counting with a surface operator and the chain-saw quiver
• A direct proof of AGT conjecture at beta = 1
• Matrix model version of AGT conjecture and generalized Selberg integrals
• Gauge Theories on ALE Space and Super Liouville Correlation Functions
• Proving the AGT relation for N_f = 0,1,2 antifundamentals
• Vertices, Vortices & Interacting Surface Operators
• The ABCDEFG of Instantons and W-algebras
• Surface Operator, Bubbling Calabi-Yau and AGT Relation
• Instantons on ALE spaces and Super Liouville Conformal Field Theories
• Supergravity one-loop corrections on AdS_7 and AdS_3, higher spins and AdS/CFT
• Matrix Models for Random Partitions
• On AGT Conjecture for Pure Super Yang-Mills and W-algebra
• The matrix model version of AGT conjecture and CIV-DV prepotential
• Non-conformal limit of AGT relation from the 1-point torus conformal block
• N=2 gauge theories and degenerate fields of Toda theory
• Towards a proof of AGT conjecture by methods of matrix models
• A review of the T_N theory and its cousins
• Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals
• Check of AGT Relation for Conformal Blocks on Sphere
• The Liouville side of the Vortex
• Massive Scaling Limit of beta-Deformed Matrix Model of Selberg Type
• Gauge Theory Wilson Loops and Conformal Toda Field Theory
• Towards R-matrix construction of Khovanov-Rozansky polynomials. I. Primary $T$-deformation of HOMFLY
• W_3 irregular states and isolated N=2 superconformal field theories
• The toroidal block and the genus expansion
• From SO/Sp instantons to W-algebra blocks
• Higher Derivative Corrections and Central Charges from Wrapped M5-branes
• Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics
• A slow review of the AGT correspondence
• Orbifolds and Exact Solutions of Strongly-Coupled Matrix Models
• Analysis of correlation functions in Toda theory and AGT-W relation for SU(3) quiver
• Wilson Loops and Chiral Correlators on Squashed Sphere
• Coset conformal blocks and N=2 gauge theories
• N=2 gauge theories on toric singularities, blow-up formulae and W-algebrae
• Exact results for $\mathcal{N}=2$ supersymmetric gauge theories on compact toric manifolds and equivariant Donaldson invariants
• On relation between Nekrasov functions and BS periods in pure SU(N) case
• N=2 Generalized Superconformal Quiver Gauge Theory
• Selberg Integral and SU(N) AGT Conjecture
• N=1 Geometries via M-theory
• Hitchin Equation, Irregular Singularity, and $N=2$ Asymptotical Free Theories
• Classical conformal blocks from TBA for the elliptic Calogero-Moser system
• Quantum Hitchin Systems via beta-deformed Matrix Models
• 't Hooft Operators in Gauge Theory from Toda CFT
• On AGT description of N=2 SCFT with N_f=4
• Liouville theory, N=2 gauge theories and accessory parameters
• Generalized matrix models and AGT correspondence at all genera
• Moore-Read Fractional Quantum Hall wavefunctions and SU(2) quiver gauge theories
• The Stringy Instanton Partition Function
• Compactification on the Ω-background and the AGT correspondence
• W(1+infinity) algebra as a symmetry behind AGT relation
• 1/4 BPS String Junctions and $N^3$ Problem in 6-dim (2,0) Superconformal Theories
• Seiberg-Witten curve via generalized matrix model
• From Liouville to Chern-Simons, Alternative Realization of Wilson Loop Operators in AGT Duality
• β-deformed matrix model and Nekrasov partition function
• $\mathcal{N}=2^{\ast }$ gauge theory, free fermions on the torus and Painlevé VI
• Large N limit of beta-ensembles and deformed Seiberg-Witten relations
• Large N techniques for Nekrasov partition functions and AGT conjecture
• Quantum Cohomology and Quantum Hydrodynamics from Supersymmetric Quiver Gauge Theories
• On the six-dimensional origin of the AGT correspondence
• ε-Corrected Seiberg-Witten Prepotential Obtained From Half Genus Expansion in beta-Deformed Matrix Model
• BPS quivers of five-dimensional SCFTs, Topological Strings and q-Painlevé equations
• Classical limit of irregular blocks and Mathieu functions
• Wilson Loops and Chiral Correlators on Squashed Spheres
• Challenges of beta-deformation
• Irregular conformal block, spectral curve and flow equations
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• $\mathcal{N}=2$ supersymmetric gauge theories on $S^2\times S^2$ and Liouville Gravity
• The gravity duals of SO/USp superconformal quivers
• Irregular matrix model with $\mathcal{W}$ symmetry
• Elliptic Genus Derivation of 4d Holomorphic Blocks
• Comments on chiral algebras and $\Omega$-deformations
• Note on refined topological vertex, Jack polynomials and instanton counting
• A Note on Wilson Loop in N=2 Quiver/M theory Gravity Duality
• Geometric transitions, double scaling limits and gauge theories
• The Euler anomaly and scale factors in Liouville/Toda CFTs
• Circular quiver gauge theories, isomonodromic deformations and $W_N$ fermions on the torus
• A note on W symmetry of N=2 gauge theory
• Proof of $A_n$ AGT conjecture at $\beta =1$