Gauge Theories and Macdonald Polynomials

Abstract

We study the N=2 four-dimensional superconformal index in various interesting limits, such that only states annihilated by more than one supercharge contribute. Extrapolating from the SU(2) generalized quivers, which have a Lagrangian description, we conjecture explicit formulae for all A-type quivers of class S, which in general do not have one. We test our proposals against several expected dualities. The index can always be interpreted as a correlator in a two-dimensional topological theory, which we identify in each limit as a certain deformation of two-dimensional Yang-Mills theory. The structure constants of the topological algebra are diagonal in the basis of Macdonald polynomials of the holonomies.

57 pages, 6 figures; v2: references added and minor improvements; v3: typos corrected

References in corpus (20)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Rigid Supersymmetric Theories in Curved Superspace
• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• 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
• On AGT relation in the case of U(3)
• Tinkertoys for Gaiotto Duality
• From 4d superconformal indices to 3d partition functions
• SQCD: A Geometric Apercu
• Relation between the 4d superconformal index and the S^3 partition function
• Proving AGT conjecture as HS duality: extension to five dimensions
• Superconformal indices for N=1 theories with multiple duals
• On the Superconformal Index of N=1 IR Fixed Points: A Holographic Check
• 3d Partition Function as Overlap of Wavefunctions
• Higgs Bundles, Gauge Theories and Quantum Groups
• Tri-vertices and SU(2)'s
• On the ISS model of dynamical SUSY breaking
• Index for Supergravity on AdS_5 \times T^{1,1} and Conifold Gauge Theory
• Supersymmetric dualities beyond the conformal window

Cited by in corpus (199)

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• N=1 Deformations and RG Flows of N=2 SCFTs
• On the Superconformal Index of Argyres-Douglas Theories
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• Chiral algebras of class S
• Down the rabbit hole with theories of class S
• Non-Lagrangian Theories from Brane Junctions
• Quantum Black Hole Entropy from 4d Supersymmetric Cardy formula
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• Tinkertoys for the Twisted D-Series
• Stress-tensor OPE in N=2 Superconformal Theories
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• Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT
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• Infrared Computations of Defect Schur Indices
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• A "Lagrangian" for a non-Lagrangian theory
• New N=1 Dualities
• T^σ_ρ(G) Theories and Their Hilbert Series
• E-String Theory on Riemann Surfaces
• Coulomb Branch Operators and Mirror Symmetry in Three Dimensions
• Chiral algebra of Argyres-Douglas theory from M5 brane
• Chiral Algebras for Trinion Theories
• VOAs labelled by complex reflection groups and 4d SCFTs
• Coulomb branch Hilbert series and Hall-Littlewood polynomials
• High-temperature asymptotics of supersymmetric partition functions
• Quiver Tails and N=1 SCFTs from M5-branes
• The exact Schur index of $\mathcal{N}=4$ SYM
• Universal Features of BPS Strings in Six-dimensional SCFTs
• On 4d rank-one N=3 superconformal field theories
• The supersymmetric index in four dimensions
• Argyres-Douglas Theories, the Macdonald Index, and an RG Inequality
• Coulomb branch Hilbert series and Three Dimensional Sicilian Theories
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• Compactifications of 6d $N=(1,0)$ SCFTs with non-trivial Stiefel-Whitney classes
• Quiver Theories for Moduli Spaces of Classical Group Nilpotent Orbits
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• Compactifications of ADE conformal matter on a torus
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• Conformal Manifolds in Four Dimensions and Chiral Algebras
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• $\mathcal{N}=2$ central charge bounds from $2d$ chiral algebras
• S-duality and the N=2 Lens Space Index
• Argyres-Douglas Theories, Chiral Algebras and Wild Hitchin Characters
• Mass-deformed $T_N$ as a linear quiver
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• On Irregular Singularity Wave Functions and Superconformal Indices
• A review of the T_N theory and its cousins
• Macdonald Index and Chiral Algebra
• 2d TQFT structure of the superconformal indices with outer-automorphism twists
• The Superconformal Index of the (2,0) Theory with Defects
• N=2 S-duality Revisited
• On Exceptional Instanton Strings
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• Gauge theories from principally extended disconnected gauge groups
• Complete Graphs, Hilbert Series, and the Higgs branch of the 4d N=2 $(A_n,A_m)$ SCFT's
• Central Charges of 2d Superconformal Defects
• The superconformal index and an elliptic algebra of surface defects
• Long Multiplet Bootstrap
• Free Field Realizations from the Higgs Branch
• Finite $N$ Corrections to the Superconformal Index of S-fold Theories
• Elliptic Blowup Equations for 6d SCFTs. II: Exceptional Cases
• Global Form of Flavor Symmetry Groups in 4d N=2 Theories of Class S
• N=1 conformal dualities
• Schur correlation functions on $S^3\times S^1$
• SCFT/VOA correspondence via $\Omega$-deformation
• Sequencing BPS Spectra
• A "Lagrangian" for the E7 Superconformal Theory
• A slow review of the AGT correspondence
• Nonunitary Lagrangians and unitary non-Lagrangian conformal field theories
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• The $\mathcal{N}=2$ Schur index from free fermions
• From 6d flows to 4d flows
• New N=1 Dualities from M5-branes and Outer-automorphism Twists
• On S-duality of the Superconformal Index on Lens Spaces and 2d TQFT
• Surface defects, the superconformal index and q-deformed Yang-Mills
• Decomposition in diverse dimensions
• Surface Defect Indices and 2d-4d BPS States
• Bootstrapping the $(A_1,A_2)$ Argyres-Douglas theory
• Magnetic quivers for rank 2 theories
• Tinkertoys for the E7 Theory
• Discrete gauge theories of charge conjugation
• Chiral Algebras, Localization and Surface Defects
• The exact Schur index in closed form
• Flavor symmetries and unitarity bounds in $\mathcal{N}=2$ SCFTs
• $\mathcal{N}=2^{\ast }$ Schur indices
• Vanishing superconformal indices and the chiral symmetry breaking
• VOAs and rank-two instanton SCFTs
• New N=1 dualities from orientifold transitions - Part I: Field Theory
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• 3d-3d correspondence for mapping tori
• 4d $\mathcal{N}=3$ indices via discrete gauging
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• Sphere correlation functions and Verma modules
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• An N=1 Lagrangian for an N=3 SCFT
• An N=1 Lagrangian for the rank 1 E6 superconformal theory
• The $\mathcal{N}=4$ Schur index with Polyakov loops
• Argyres-Douglas Theories in Class S Without Irregularity
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• Four-dimensional Lens Space Index from Two-dimensional Chiral Algebra
• On the Correspondence between Surface Operators in Argyres-Douglas Theories and Modules of Chiral Algebra
• Heterotic Surface Defects and Dualities from 2d/4d Indices
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• The moduli space of instantons on an ALE space from 3d $\mathcal{N}=4$ field theories
• Vanishing OPE Coefficients in 4d N=2 SCFTs
• Needles in a haystack: An algorithmic approach to the classification of 4d $\mathcal{N}=2$ SCFTs
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• Minimal $(D,D)$ conformal matter and generalizations of the van Diejen model
• A brief review of the 2d/4d correspondences
• Quiver Theories and Hilbert Series of Classical Slodowy Intersections
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• Distinguishing 6d (1,0) SCFTs: an extension to the geometric construction
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• Higgs, Coulomb, and Hall-Littlewood
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• On Three-Dimensional Quiver Gauge Theories of Type B
• q-deformations of two-dimensional Yang-Mills theory: Classification, categorification and refinement
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• Structure of Anomalies of 4d SCFTs from M5-branes, and Anomaly Inflow
• A Small Deformation of a Simple Theory
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• Surface defects, flavored modular differential equations and modularity
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• Large $N$ and large representations of Schur line defect correlators
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• 3d mirrors of the circle reduction of twisted $A_{2N}$ theories of class $\mathsf{S}$
• Wrapped Branes and Punctured Horizons
• Star shaped quivers with flux
• Brane webs in the presence of an $O{5}^{-}$-plane and 4d class S theories of type D
• Differential operators for superconformal correlation functions
• Flowing from 16 to 32 Supercharges
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• Supersymmetric Casimir Energy and $\mathrm{SL}(3,\mathbb{Z})$ Transformations
• The Coulomb and Higgs Branches of $\mathcal{N}=1$ Theories of Class ${\mathcal{S}}_k$
• On Classical Solutions of 4d Supersymmetric Higher Spin Theory
• Superconformal index with surface defects for class ${\mathcal{S}}_k$
• $\mathcal{N}=1$ Liouville SCFT in Four Dimensions
• OPE Selection Rules for Schur Multiplets in 4D $\mathcal{N}=2$ Superconformal Field Theories
• Excitations of bubbling geometries for line defects
• A new rank-2 Argyres-Douglas theory
• Eta Products, BPS States and K3 Surfaces
• A freely generated ring for N=1 models in class S_k
• Testing Macdonald Index as a Refined Character of Chiral Algebra
• Closed form fermionic expressions for the Macdonald index
• The Chiral Algebra of Genus Two Class $\mathcal{S}$ Theory
• 5d gauge theories on orbifolds and 4d 't Hooft line indices
• 3d SUSY enhancement and non-semisimple TQFTs from four dimensions
• Deformation quantizations from vertex operator algebras
• Refined Chern-Simons theory and (q,t)-deformed Yang-Mills theory: Semi-classical expansion and planar limit
• Emergent N=4 supersymmetry from N=1
• On the Protected Spectrum of the Minimal Argyres-Douglas Theory
• $C_2$ generalization of the van Diejen model from the minimal $(D_5,D_5)$ conformal matter
• Equivariant U(N) Verlinde algebra from Bethe/Gauge correspondence
• Macdonald Indices for Four-dimensional $\mathcal{N}=3$ Theories
• An infrared bootstrap of the Schur index with surface defects
• Root of unity asymptotics for Schur indices of 4d Lagrangian theories
• Peculiar Index Relations, 2D TQFT, and Universality of SUSY Enhancement
• The NS limit of the 5D Superconformal Index
• Argyres-Douglas Avatars of Coulomb Branch Physics
• Wilson punctured network defects in 2D q-deformed Yang-Mills theory
• Five-dimensional cohomological localization and squashed $q$-deformations of two-dimensional Yang-Mills theory
• Ground state wavefunctions of elliptic relativistic integrable Hamiltonians
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• A Family of Vertex Algebras from Argyres-Douglas Theory
• Quiver Polymerisation
• Orbifold Schur Index and IR formula
• Topological Field Theory Amplitudes for $A_{N-1}$ Fibration
• Chiral expansion and Macdonald deformation of two-dimensional Yang-Mills theory
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• Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs
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• New Dualities and Misleading Anomaly Matchings from Outer-automorphism Twists
• Twisted chiral algebras of class $\mathcal{S}$ and mixed Feigin-Frenkel gluing
• Supersymmetric zeta functions and determinants
• $S^1$ Reduction of 4D $\mathcal{N}=3$ SCFTs and Squashing Independence of ABJM Theories
• BPS index and 4d N=2 superconformal field theories
• Schur Connections: Chord Counting, Line Operators, and Indices
• Aspects of 4d supersymmetric dynamics and geometry
• Macdonald Index From Refined Kontsevich-Soibelman Operator
• Factorized class $S$ theories and surface defects
• Orbi-Instantons and Class $\mathcal{S}$ Theories of Type D