Infinitely many 4d $\mathcal{N}=2$ SCFTs with $a=c$ and beyond

Abstract

We study a set of four-dimensional $\mathcal{N}=2$ superconformal field theories (SCFTs) $\hat{\Gamma }(G)$ labeled by a pair of simply-laced Lie groups $\Gamma$ and $G$. They are constructed out of gauging a number of ${\mathcal{D}}_p(G)$ and $(G,G)$ conformal matter SCFTs; therefore they do not have Lagrangian descriptions in general. For $\Gamma =D_4,E_6,E_7,E_8$ and some special choices of $G$, the resulting theories have identical central charges $(a=c)$ without taking any large $N$ limit. Moreover, we find that the Schur indices for such theories can be written in terms of that of $\mathcal{N}=4$ super Yang--Mills theory upon rescaling fugacities. Especially, we find that the Schur index of ${\hat{D}}_4(SU(N))$ theory for $N$ odd is written in terms of MacMahon's generalized sum-of-divisor function, which is quasi-modular. For generic choices of $\Gamma$ and $G$, it can be regarded as a generalization of the affine quiver gauge theory obtained from $D3$-branes probing an ALE singularity of type $\Gamma$. We also comment on a tantalizing connection regarding the theories labeled by $\Gamma$ in the Deligne--Cvitanović exceptional series.

arXiv comment33pages+appendix, 8 tables, 4 figures

References in corpus (95)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Generalized Global Symmetries
• Liouville Correlation Functions from Four-dimensional Gauge Theories
• N=2 dualities
• An Index for 4 dimensional Super Conformal Theories
• D-branes, Quivers, and ALE Instantons
• 4d Conformal Field Theories and Strings on Orbifolds
• New Phenomena in SU(3) Supersymmetric Gauge Theory
• Infinite Chiral Symmetry in Four Dimensions
• F-theory and Orientifolds
• Reading between the lines of four-dimensional gauge theories
• Counting chiral primaries in N=1 d=4 superconformal field theories
• New N=2 Superconformal Field Theories in Four Dimensions
• On the Classification of 6D SCFTs and Generalized ADE Orbifolds
• Gauge Theories and Macdonald Polynomials
• On Short and Semi-Short Representations for Four Dimensional Superconformal Symmetry
• Beyond eta/s = 1/4pi
• An N=2 Superconformal Fixed Point with E_6 Global Symmetry
• Atomic Classification of 6D SCFTs
• 6d Conformal Matter
• S-duality in N=2 supersymmetric gauge theories
• The 4d Superconformal Index from q-deformed 2d Yang-Mills
• Superconformal Fixed Points with E_n Global Symmetry
• S-duality and 2d Topological QFT
• F-Theory at Constant Coupling
• Probing F-theory With Branes
• Nilpotent orbits and codimension-two defects of 6d N=(2,0) theories
• R-Twisting and 4d/2d Correspondences
• General Argyres-Douglas Theory
• Tinkertoys for Gaiotto Duality
• Anomaly polynomial of general 6d SCFTs
• Cardy Formulae for SUSY Theories in d=4 and d=6
• Central charges of N=2 superconformal field theories in four dimensions
• N=1 Deformations and RG Flows of N=2 SCFTs
• Enhancement of Supersymmetry via Renormalization Group Flow and the Superconformal Index
• On the Superconformal Index of Argyres-Douglas Theories
• Wild Quiver Gauge Theories
• Irregular singularities in Liouville theory
• 5d Superconformal Field Theories and Graphs
• Geometric Engineering, Mirror Symmetry and 6d (1,0) -> 4d, N=2
• Coulomb and Higgs Branches from Canonical Singularities: Part 0
• N=1 Deformations and RG Flows of N=2 SCFTs, Part II: Non-principal deformations
• Fibers add Flavor, Part I: Classification of 5d SCFTs, Flavor Symmetries and BPS States
• Six-dimensional D_N theory and four-dimensional SO-USp quivers
• The asymptotic growth of states of the 4d N=1 superconformal index
• 5d and 4d SCFTs: Canonical Singularities, Trinions and S-Dualities
• More on the N=2 superconformal systems of type $D_p(G)$
• A 4d N=1 Cardy Formula
• Classification of Argyres-Douglas theories from M5 branes
• Exceptional Indices
• Fibers add Flavor, Part II: 5d SCFTs, Gauge Theories, and Dualities
• Superconformal indices of generalized Argyres-Douglas theories from 2d TQFT
• Infinitely many N=2 SCFT with ADE flavor symmetry
• 6d, N=(1,0) Coulomb Branch Anomaly Matching
• Vertex operator algebras of Argyres-Douglas theories from M5-branes
• EFT and the SUSY Index on the 2nd Sheet
• Chiral algebra of Argyres-Douglas theory from M5 brane
• N=1 Lagrangians for generalized Argyres-Douglas theories
• High-temperature asymptotics of supersymmetric partition functions
• Universal Features of BPS Strings in Six-dimensional SCFTs
• Argyres-Douglas Theories, the Macdonald Index, and an RG Inequality
• Codimension-two defects and Argyres-Douglas theories from outer-automorphism twist in 6d $(2,0)$ theories
• Higher Form Symmetries of Argyres-Douglas Theories
• Conformal Manifolds in Four Dimensions and Chiral Algebras
• Fission, Fusion, and 6D RG Flows
• On Irregular Singularity Wave Functions and Superconformal Indices
• Macdonald Index and Chiral Algebra
• RG flows with supersymmetry enhancement and geometric engineering
• Free Field Realizations from the Higgs Branch
• Positivity, negativity, and entanglement
• Nonunitary Lagrangians and unitary non-Lagrangian conformal field theories
• From 6d flows to 4d flows
• T-Branes, String Junctions, and 6D SCFTs
• Tinkertoys for the E7 Theory
• On four dimensional N=3 superconformal theories
• Schur sector of Argyres-Douglas theory and $W$-algebra
• 6D SCFTs, 4D SCFTs, Conformal Matter, and Spin Chains
• Vanishing OPE Coefficients in 4d N=2 SCFTs
• Flopping and Slicing: SO(4) and Spin(4)-models
• M-theory on Elliptic Calabi-Yau Threefolds and 6d Anomalies
• F-theory and Unpaired Tensors in 6D SCFTs and LSTs
• The Geometry of the SU(2)$\times$ G${}_2$-model
• Argyres-Douglas matter and N=2 dualities
• Argyres-Douglas matter and S-duality: Part II
• The Geometry of SO(3), SO(5), and SO(6) models
• The Geometry of G${}_2$, Spin(7), and Spin(8)-models
• Classification of large N superconformal gauge theories with a dense spectrum
• Testing Macdonald Index as a Refined Character of Chiral Algebra
• Closed form fermionic expressions for the Macdonald index
• Argyres-Douglas Theories, S-duality and AGT Correspondence
• 48 Crepant Paths to $\text{SU}(2)\times \text{SU}(3)$
• Macdonald Indices for Four-dimensional $\mathcal{N}=3$ Theories
• New N = 2 dualities
• The suspended pinch point and SU($2$)$\times$U($1$) gauge theories
• $\mathcal{N}=4$ SYM, Argyres-Douglas Theories, and an Exact Graded Vector Space Isomorphism

Cited by in corpus (10)

• 6d SCFTs, Center-Flavor Symmetries, and Stiefel--Whitney Compactifications
• The exact Schur index in closed form
• $\mathcal{N}=2^{\ast }$ Schur indices
• Holographic duals of M5-branes on an irregularly punctured sphere
• Higgs, Coulomb, and Hall-Littlewood
• Modular Anomaly Equation for Schur Index of $\mathcal{N}=4$ Super-Yang-Mills
• Infinitely many 4d N=1 SCFTs with a=c
• Emergent N=4 supersymmetry from N=1
• Generalized symmetry constraints on deformed 4d (S)CFTs
• A landscape of 4d N=1 SCFTs with a=c