Testing our understanding of SCFTs: a catalogue of rank-2 $\mathcal{N}$=2 theories in four dimensions

Abstract

In this paper we begin mapping out the space of rank-2 $\mathcal{N}=2$ superconformal field theories (SCFTs) in four dimensions. This represents an ideal set of theories which can be potentially classified using purely quantum field-theoretic tools, thus providing a precious case study to probe the completeness of the current understanding of SCFTs, primarily derived from string theory constructions. Here, we collect and systematize a large amount of field theoretic data characterizing each theory. We also provide a detailed description of each case and determine the theories' Coulomb, Higgs and Mixed branch stratification. The theories naturally organize themselves into series connected by RG flows but which have gaps suggesting that our current understanding is not complete.

arXiv commentCorrecting a few tables and Hasse diagrams, few references added

References in corpus (107)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories
• N=2 dualities
• Supersymmetric Yang-Mills Systems And Integrable Systems
• Five Dimensional SUSY Field Theories, Non-trivial Fixed Points and String Dynamics
• Infinite Chiral Symmetry in Four Dimensions
• Open P-Branes
• F-theory and Orientifolds
• Reading between the lines of four-dimensional gauge theories
• Extremal Transitions and Five-Dimensional Supersymmetric Field Theories
• Five-Dimensional Supersymmetric Gauge Theories and Degenerations of Calabi-Yau Spaces
• Some Comments On String Dynamics
• The Moduli Space of N=2 SUSY QCD and Duality in N=1 SUSY QCD
• Wall-crossing, Hitchin Systems, and the WKB Approximation
• On the Classification of 6D SCFTs and Generalized ADE Orbifolds
• An N=2 Superconformal Fixed Point with E_6 Global Symmetry
• Atomic Classification of 6D SCFTs
• 6d Conformal Matter
• Symplectic singularities
• Introduction to S-Duality in N=2 Supersymmetric Gauge Theory. (A pedagogical review of the work of Seiberg and Witten)
• Superconformal Fixed Points with E_n Global Symmetry
• F-Theory at Constant Coupling
• Non-trivial Fixed Points of The Renormalization Group in Six Dimensions
• 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
• Small Instantons, del Pezzo Surfaces and Type I' theory
• The Vacuum Structure of N=2 SuperQCD with Classical Gauge Groups
• Study of $N=2$ Superconformal Field Theories in $4$ Dimensions
• Tinkertoys for Gaiotto Duality
• Schur Indices, BPS Particles, and Argyres-Douglas Theories
• On Geometric Classification of 5d SCFTs
• Special Kahler Manifolds
• Notes on Theories with 16 Supercharges
• Central charges of N=2 superconformal field theories in four dimensions
• Vertex operator algebras, Higgs branches, and modular differential equations
• Deformations of Superconformal Theories
• N=3 four dimensional field theories
• Introduction to Seiberg-Witten Theory and its Stringy Origin
• Tinkertoys for the D_N series
• 5d Superconformal Field Theories and Graphs
• S-folds and 4d N=3 superconformal field theories
• Coulomb and Higgs Branches from Canonical Singularities: Part 0
• Fibers add Flavor, Part I: Classification of 5d SCFTs, Flavor Symmetries and BPS States
• Top Down Approach to 6D SCFTs
• More on the N=2 superconformal systems of type $D_p(G)$
• On S-duality of 5d super Yang-Mills on S^1
• The Higgs Mechanism -- Hasse Diagrams for Symplectic Singularities
• Tinkertoys for the Twisted D-Series
• Probing F-theory With Multiple Branes
• Fibers add Flavor, Part II: 5d SCFTs, Gauge Theories, and Dualities
• Infinitely many N=2 SCFT with ADE flavor symmetry
• Rationality of W-algebras: principal nilpotent cases
• Quiver Subtractions
• Twisted Circle Compactifications of 6d SCFTs
• Chiral algebra of Argyres-Douglas theory from M5 brane
• 4d $\mathcal{N}$=2 theories with disconnected gauge groups
• Geometric constraints on the space of N=2 SCFTs I: physical constraints on relevant deformations
• Classification of 4d N=2 gauge theories
• Magnetic quivers for rank 1 theories
• Compactifications of 6d $N=(1,0)$ SCFTs with non-trivial Stiefel-Whitney classes
• Codimension-two defects and Argyres-Douglas theories from outer-automorphism twist in 6d $(2,0)$ theories
• Geometric classification of 4d $\mathcal{N}=2$ SCFTs
• 4d $\mathcal{N}=2$ S-folds
• Finite-Dimensional Lie Algebras and Their Representations for Unified Model Building
• Revisiting the classifications of 6d SCFTs and LSTs
• Gauge theories from principally extended disconnected gauge groups
• Discrete complex reflection groups
• S-fold magnetic quivers
• Seiberg-Witten geometries for Coulomb branch chiral rings which are not freely generated
• RG flows with supersymmetry enhancement and geometric engineering
• Free Field Realizations from the Higgs Branch
• Gaiotto Duality for the Twisted A_{2N-1} Series
• Towards Classification of 5d SCFTs: Single Gauge Node
• New N=2 superconformal field theories from S-folds
• Towards a classification of rank $r$ $\mathcal{N}=2$ SCFTs Part II: special Kahler stratification of the Coulomb branch
• Magnetic quivers for rank 2 theories
• Tinkertoys for the E7 Theory
• Hasse Diagrams for $3d$ $\mathcal{N}=4$ Quiver Gauge Theories -- Inversion and the full Moduli Space
• Self-dual strings in six dimensions: Anomalies, the ADE-classification, and the world-sheet WZW-model
• S-folds, String Junctions, and 4D $\mathcal{N}=2$ SCFTs
• Geometric constraints on the space of N=2 SCFTs III: enhanced Coulomb branches and central charges
• VOAs and rank-two instanton SCFTs
• Supersymmetric Gauge Theories from Branes and Orientifold Six-planes
• The Singularity Structure of Scale-Invariant Rank-2 Coulomb Branches
• Towards the classification of rank-$r$ $\mathcal{N}=2$ SCFTs. Part I: twisted partition function and central charge formulae
• Geometric constraints on the space of N=2 SCFTs II: Construction of special Kähler geometries and RG flows
• Coulomb branches with complex singularities
• Argyres-Douglas Theories in Class S Without Irregularity
• Needles in a haystack: An algorithmic approach to the classification of 4d $\mathcal{N}=2$ SCFTs
• Tinkertoys for the Twisted $E_6$ Theory
• A Family of $4D$ $\mathcal{N}=2$ Interacting SCFTs from the Twisted $A_{2N}$ Series
• Compactifications of 5d SCFTs with a twist
• On the compactification of 5d theories to 4d
• Scaling dimensions of Coulomb branch operators of 4d N=2 superconformal field theories
• Classification of N=2 Superconformal Field Theories with Two-Dimensional Coulomb Branches
• Classification of all $\mathcal{N}\ge 3$ moduli space orbifold geometries at rank 2
• Construction and classification of Coulomb branch geometries
• Expanding the landscape of $\mathcal{N}$=2 rank 1 SCFTs
• Modular representations of reductive groups and geometry of affine Grassmannians
• A new rank-2 Argyres-Douglas theory
• Tinkertoys for the $E_8$ Theory
• On the moduli spaces of 4d $\mathcal{N}=3$ SCFTs I: triple special Kähler structure
• The constraining power of Coulomb Branch Geometry: lectures on Seiberg-Witten theory
• Four-dimensional $N=1$ theories, S-fold constraints on T-branes, and behaviors in IR and UV

Cited by in corpus (13)

• 6d SCFTs, Center-Flavor Symmetries, and Stiefel--Whitney Compactifications
• Fibrations and Hasse diagrams for 6d SCFTs
• Dirac pairings, one-form symmetries and Seiberg-Witten geometries
• Higgs branch RG-flows via Decay and Fission
• The Characteristic Dimension of Four-dimensional $\mathcal{N}=2$ SCFTs
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• Partition functions of non-Lagrangian theories from the holomorphic anomaly
• Exceptional moduli spaces for exceptional $\mathcal{N}=3$ theories
• Coulomb branch surgery: Holonomy saddles, S-folds and discrete symmetry gaugings
• Electric-Magnetic Duality in a Class of $G_2$-Compactifications of M-theory
• Aspects of 4d supersymmetric dynamics and geometry
• Completely (iso-)split scale-invariant Coulomb branch geometries are isotrivial
• FI-flows of 3d N=4 Theories