2D CFT blocks for the 4D class ${\mathcal{S}}_k$ theories

Abstract

This is the first in a series of papers on the search for the 2D CFT description of a large class of 4D $\mathcal{N}=1$ gauge theories. Here, we identify the 2D CFT symmetry algebra and its representations, namely the conformal blocks of the Virasoro/W-algebra, that underlie the 2D theory and reproduce the Seiberg-Witten curves of the $\mathcal{N}=1$ gauge theories. We find that the blocks corresponding to the SU(N) ${\mathcal{S}}_k$ gauge theories involve fields in certain non-unitary representations of the $W_{kN}$ algebra. These conformal blocks give a prediction for the instanton partition functions of the 4D $\mathcal{N}=1$ SCFTs of class ${\mathcal{S}}_k$.

arXiv comment42 pages,5 figures

References in corpus (62)

• 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
• 4d Conformal Field Theories and Strings on Orbifolds
• Exactly Marginal Operators and Duality in Four Dimensional N=1 Supersymmetric Gauge Theory
• W-symmetry in Conformal Field Theory
• Lectures on supersymmetric gauge theories and electric-magnetic duality
• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• On Conformal Theories in Four Dimensions
• Loop and surface operators in N=2 gauge theory and Liouville modular geometry
• Wall-crossing, Hitchin Systems, and the WKB Approximation
• The Calculus of Many Instantons
• Phases of N=1 supersymmetric gauge theories in four dimensions
• Large N limit of orbifold field theories
• Exactly Marginal Deformations and Global Symmetries
• Sphere Partition Functions and the Zamolodchikov Metric
• String Expansion as Large N Expansion of Gauge Theories
• Correlation functions in conformal Toda field theory I
• Seiberg-Witten Theories on Ellipsoids
• Para-Liouville/Toda central charges from M5-branes
• A & B model approaches to surface operators and Toda theories
• Geometrically Induced Metastability and Holography
• Non-Lagrangian Theories from Brane Junctions
• Liouville theory with a central charge less than one
• M5-branes, toric diagrams and gauge theory duality
• Super Liouville conformal blocks from N=2 SU(2) quiver gauge theories
• Holography for $\mathcal{N}=2^{\ast }$ on $S^4$
• Instanton moduli spaces and bases in coset conformal field theory
• Gauge Theories on ALE Space and Super Liouville Correlation Functions
• BPS/CFT Correspondence III: Gauge Origami partition function and qq-characters
• Integrable structure, W-symmetry and AGT relation
• The ABCDEFG of Instantons and W-algebras
• Instantons on ALE spaces and Super Liouville Conformal Field Theories
• Chiral Gauge Theories from D-Branes
• Exact Bremsstrahlung and Effective Couplings
• N=2 gauge theories and degenerate fields of Toda theory
• The Exact Effective Couplings of 4D N=2 gauge theories
• The Veneziano Limit of N=2 Superconformal QCD: Towards the String Dual of N=2 SU(N_c) SYM with N_f =2 N_c
• Holography for $\mathcal{N}=1^{\ast }$ on $S^4$
• Charting Class ${\mathcal{S}}_k$ Territory
• F-Theory and N=1 SCFTs in Four Dimensions
• Integrability in N=2 superconformal gauge theories
• Chiral theories of class S
• Parafermionic Liouville field theory and instantons on ALE spaces
• Surface defects and elliptic quantum groups
• Coset conformal blocks and N=2 gauge theories
• From 6D SCFTs to Dynamic GLSMs
• From N=4 gauge theory to N=2 conformal QCD: three-loop mixing of scalar composite operators
• N=1 theories of class S_k
• Toda Theory From Six Dimensions
• Punctures for Theories of Class ${\mathcal{S}}_{\Gamma }$
• Spin Chains in N=2 Superconformal Theories: from the Z_2 Quiver to Superconformal QCD
• M(ore) on Chiral Gauge Theories from D-Branes
• The Complete One-Loop Dilation Operator of N=2 SuperConformal QCD
• S-duality in $\mathcal{N}=1$ orientifold SCFTs
• 4d N=1 from 6d N=(1,0) on a torus with fluxes
• Extended Supersymmetric Moduli Space and a SUSY/Non-SUSY Duality
• Superconformal index with surface defects for class ${\mathcal{S}}_k$
• New Dualities and Misleading Anomaly Matchings from Outer-automorphism Twists

Cited by in corpus (12)

• A slow review of the AGT correspondence
• From 6d flows to 4d flows
• Conformal manifolds: ODEs from OPEs
• An $\mathcal{N}=1$ 3d-3d Correspondence
• Quasi-Jacobi Forms, Elliptic Genera and Strings in Four Dimensions
• The Coulomb and Higgs Branches of $\mathcal{N}=1$ Theories of Class ${\mathcal{S}}_k$
• A freely generated ring for N=1 models in class S_k
• Deconstructing Little Strings with $\mathcal{N}=1$ Gauge Theories on Ellipsoids
• $\mathcal{N}=1$ Curves on Generalized Coulomb Branches
• Punctures and Dynamical Systems
• Partition Functions of $\mathcal{N}=1$ Gauge Theories on $S^2\times {\mathbb{R}}_{\epsilon }^2$ and Duality
• Aspects of 4d supersymmetric dynamics and geometry