Chiral algebras of class S

Abstract

Four-dimensional N=2 superconformal field theories have families of protected correlation functions that possess the structure of two-dimensional chiral algebras. In this paper, we explore the chiral algebras that arise in this manner in the context of theories of class S. The class S duality web implies nontrivial associativity properties for the corresponding chiral algebras, the structure of which is best summarized in the language of generalized topological quantum field theory. We make a number of conjectures regarding the chiral algebras associated to various strongly coupled fixed points.

47+15 pages, 9 figures, 6 tables. v2: Conjecture 1 modified to accommodate new data. Some typos corrected

References in corpus (6)

• Infinite Chiral Symmetry in Four Dimensions
• S-duality in N=2 supersymmetric gauge theories
• Webs of five-branes and N=2 superconformal field theories
• The 4d Superconformal Index from q-deformed 2d Yang-Mills
• Tinkertoys for Gaiotto Duality
• Chiral Algebras for Trinion Theories

Cited by in corpus (80)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Infinite Chiral Symmetry in Four Dimensions
• Schur Indices, BPS Particles, and Argyres-Douglas Theories
• W Symmetry in six dimensions
• Vertex operator algebras, Higgs branches, and modular differential equations
• Tensionless String Spectra on ${\mathrm{AdS}}_3$
• N=1 Deformations and RG Flows of N=2 SCFTs
• The $\mathcal{N}=2$ superconformal bootstrap
• Bootstrapping SCFTs with Four Supercharges
• Deformation quantization and superconformal symmetry in three dimensions
• Stress-tensor OPE in N=2 Superconformal Theories
• Surface Defects and Chiral Algebras
• Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT
• Infrared Computations of Defect Schur Indices
• Conformal Collider Physics from the Lightcone Bootstrap
• Bootstrapping $\mathcal{N}=3$ superconformal theories
• Vertex operator algebras of Argyres-Douglas theories from M5-branes
• Vertex Operator Algebras and 3d N=4 gauge theories
• Chiral algebra of Argyres-Douglas theory from M5 brane
• 4d $\mathcal{N}$=2 theories with disconnected gauge groups
• VOAs labelled by complex reflection groups and 4d SCFTs
• Universal Features of BPS Strings in Six-dimensional SCFTs
• On 4d rank-one N=3 superconformal field theories
• Webs of W-algebras
• On Superconformal Four-Point Mellin Amplitudes in Dimension $d>2$
• Superconformal surfaces in four dimensions
• $\mathcal{N}=2$ central charge bounds from $2d$ chiral algebras
• Argyres-Douglas Theories, Chiral Algebras and Wild Hitchin Characters
• Non-Abelian Binding Energies from the Lightcone Bootstrap
• Macdonald Index and Chiral Algebra
• Gauge theories from principally extended disconnected gauge groups
• Seiberg-Witten geometries for Coulomb branch chiral rings which are not freely generated
• Logarithmic W-algebras and Argyres-Douglas theories at higher rank
• Free Field Realizations from the Higgs Branch
• Central Charges of 2d Superconformal Defects
• Elliptic Blowup Equations for 6d SCFTs. II: Exceptional Cases
• SCFT/VOA correspondence via $\Omega$-deformation
• Schur correlation functions on $S^3\times S^1$
• A slow review of the AGT correspondence
• New N=2 superconformal field theories from S-folds
• Surface Defect Indices and 2d-4d BPS States
• The exact Schur index in closed form
• Chiral Algebras, Localization and Surface Defects
• Exploring the Minimal 4D $\mathcal{N}=1$ SCFT
• Flavor symmetries and unitarity bounds in $\mathcal{N}=2$ SCFTs
• VOAs and rank-two instanton SCFTs
• Rationalizing CFTs and Anyonic Imprints on Higgs Branches
• Schur sector of Argyres-Douglas theory and $W$-algebra
• Argyres-Douglas Theories in Class S Without Irregularity
• On the Correspondence between Surface Operators in Argyres-Douglas Theories and Modules of Chiral Algebra
• Four-dimensional Lens Space Index from Two-dimensional Chiral Algebra
• Abelian dualities of $\mathcal{N}=(0,4)$ boundary conditions
• Compactifications of 5d SCFTs with a twist
• Distinguishing 6d (1,0) SCFTs: an extension to the geometric construction
• More on holographic correlators: Twisted and dimensionally reduced structures
• Bose-Fermi cancellations without supersymmetry
• Surface defects, flavored modular differential equations and modularity
• Differential operators for superconformal correlation functions
• Classification of all $\mathcal{N}\ge 3$ moduli space orbifold geometries at rank 2
• OPE Selection Rules for Schur Multiplets in 4D $\mathcal{N}=2$ Superconformal Field Theories
• Defects, modular differential equations, and free field realization of N = 4 VOAs
• A new rank-2 Argyres-Douglas theory
• Coulomb Branches of Star-Shaped Quivers
• The Chiral Algebra of Genus Two Class $\mathcal{S}$ Theory
• A CFT Distance Conjecture
• Rationality of the exceptional W-algebras ${\mathcal{W}}_k({\mathfrak{sp}}_4,f_{subreg})$ associated with subregular nilpotent elements of ${\mathfrak{sp}}_4$
• Closed form fermionic expressions for the Macdonald index
• Deformation quantizations from vertex operator algebras
• Peculiar Index Relations, 2D TQFT, and Universality of SUSY Enhancement
• Affine $\mathcal{W}$-algebras and Miura maps from 3d $\mathcal{N}=4$ non-Abelian quiver gauge theories
• Flavor symmetries and the topology of special Kähler structures at rank 1
• Free field realisation and the chiral universal centraliser
• A Family of Vertex Algebras from Argyres-Douglas Theory
• Toward Null State Equations in $d>2$
• Orbifold Schur Index and IR formula
• Derived gluing construction of chiral algebras
• Fermionic extensions of $W$-algebras via 3d $\mathcal{N}=4$ gauge theories with a boundary
• Twisted chiral algebras of class $\mathcal{S}$ and mixed Feigin-Frenkel gluing
• Schur correlation functions from q-deformed Yang-Mills
• Rebooting quarter-BPS operators in $\mathcal{N}=4$ Super Yang-Mills