N=2 gauge theories and degenerate fields of Toda theory

Abstract

We discuss the correspondence between degenerate fields of the W_N algebra and punctures of Gaiotto's description of the Seiberg-Witten curve of N=2 superconformal gauge theories. Namely, we find that the type of degenerate fields of the W_N algebra, with null states at level one, is classified by Young diagrams with N boxes, and that the singular behavior of the Seiberg-Witten curve near the puncture agrees with that of W_N generators. We also find how to translate mass parameters of the gauge theory to the momenta of the Toda theory.

23 pages,v2: minor corrections,published version

References in corpus (9)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• On AGT relation in the case of U(3)
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• Correlation functions in conformal Toda field theory I
• Para-Liouville/Toda central charges from M5-branes
• The Quiver Matrix Model and 2d-4d Conformal Connection
• Hitchin systems, N=2 gauge theories and W-gravity
• Hitchin Equation, Singularity, and N=2 Superconformal Field Theories

Cited by in corpus (49)

• Vortex Counting and Lagrangian 3-manifolds
• Four-Dimensional SCFTs from M5-Branes
• The Virtue of Defects in 4D Gauge Theories and 2D CFTs
• Wild Quiver Gauge Theories
• Matrix Model Conjecture for Exact BS Periods and Nekrasov Functions
• A & B model approaches to surface operators and Toda theories
• Conformal blocks as Dotsenko-Fateev Integral Discriminants
• Proving AGT conjecture as HS duality: extension to five dimensions
• 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
• A direct proof of AGT conjecture at beta = 1
• Matrix model version of AGT conjecture and generalized Selberg integrals
• Proving the AGT relation for N_f = 0,1,2 antifundamentals
• Affine sl(N) conformal blocks from N=2 SU(N) gauge theories
• The matrix model version of AGT conjecture and CIV-DV prepotential
• On AGT Conjecture for Pure Super Yang-Mills and W-algebra
• Towards a proof of AGT conjecture by methods of matrix models
• Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals
• On "Dotsenko-Fateev" representation of the toric conformal blocks
• Check of AGT Relation for Conformal Blocks on Sphere
• Gauge Theory Wilson Loops and Conformal Toda Field Theory
• W_3 irregular states and isolated N=2 superconformal field theories
• A slow review of the AGT correspondence
• Analysis of correlation functions in Toda theory and AGT-W relation for SU(3) quiver
• Coset conformal blocks and N=2 gauge theories
• On relation between Nekrasov functions and BS periods in pure SU(N) case
• Quarter-BPS AdS5 solutions in M-theory with a T2 bundle over a Riemann surface
• N=2 Generalized Superconformal Quiver Gauge Theory
• Hitchin Equation, Irregular Singularity, and $N=2$ Asymptotical Free Theories
• ADE Little String Theory on a Riemann Surface (and Triality)
• On AGT description of N=2 SCFT with N_f=4
• On W-algebras and the symmetries of defects of 6d N=(2,0) theory
• Compactification on the Ω-background and the AGT correspondence
• W(1+infinity) algebra as a symmetry behind AGT relation
• 2D CFT blocks for the 4D class ${\mathcal{S}}_k$ theories
• W-algebras and surface operators in N=2 gauge theories
• Triality in SU(2) Seiberg-Witten theory and Gauss hypergeometric function
• (de)Tails of Toda CFT
• Irregular conformal block, spectral curve and flow equations
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• The ABCDEFG of Little Strings
• Little String Defects and Bala-Carter Theory
• Irregular matrix model with $\mathcal{W}$ symmetry
• Notes on 3-point functions of A_{N-1} Toda theory and AGT-W relation for SU(N) quiver
• Masses, Sheets and Rigid SCFTs
• $\widehat{\mathfrak{sl}}(n{)}_N$ WZW conformal blocks from $SU(N)$ instanton partition functions on ${\mathbb{C}}^2/{\mathbb{Z}}_n$
• Irregular Singularities in the H3+ WZW Model
• The Euler anomaly and scale factors in Liouville/Toda CFTs
• A note on W symmetry of N=2 gauge theory