On the Classification of 6D SCFTs and Generalized ADE Orbifolds

Abstract

We study (1,0) and (2,0) 6D superconformal field theories (SCFTs) that can be constructed in F-theory. Quite surprisingly, all of them involve an orbifold singularity C^2 / G with G a discrete subgroup of U(2). When G is a subgroup of SU(2), all discrete subgroups are allowed, and this leads to the familiar ADE classification of (2,0) SCFTs. For more general U(2) subgroups, the allowed possibilities for G are not arbitrary and are given by certain generalizations of the A- and D-series. These theories should be viewed as the minimal 6D SCFTs. We obtain all other SCFTs by bringing in a number of E-string theories and/or decorating curves in the base by non-minimal gauge algebras. In this way we obtain a vast number of new 6D SCFTs, and we conjecture that our construction provides a full list.

v3: 47 pages, 3 figures, clarifications added, typos corrected, references added, and Mathematica file updated

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Cited by in corpus (219)

• Atomic Classification of 6D SCFTs
• 6d Conformal Matter
• Tensionless Strings and the Weak Gravity Conjecture
• On Geometric Classification of 5d SCFTs
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• F-Theory on all Toric Hypersurface Fibrations and its Higgs Branches
• On the Defect Group of a 6D SCFT
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• Geometric Engineering, Mirror Symmetry and 6d (1,0) -> 4d, N=2
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• The Branes Behind Generalized Symmetry Operators
• Fibers add Flavor, Part I: Classification of 5d SCFTs, Flavor Symmetries and BPS States
• Top Down Approach to 6D SCFTs
• Strings of Minimal 6d SCFTs
• Classifying 5d SCFTs via 6d SCFTs: Arbitrary rank
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• F-theory and the Classification of Little Strings
• Fibers add Flavor, Part II: 5d SCFTs, Gauge Theories, and Dualities
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• Elliptic Genus of E-strings
• Chern-Weil Global Symmetries and How Quantum Gravity Avoids Them
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• F-Theory, Spinning Black Holes and Multi-string Branches
• $E_8$ instantons on type-A ALE spaces and supersymmetric field theories
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• 6d, N=(1,0) Coulomb Branch Anomaly Matching
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• 6D RG Flows and Nilpotent Hierarchies
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• Refined BPS invariants of 6d SCFTs from anomalies and modularity
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• Tao Probing the End of the World
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• On Exceptional Instanton Strings
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• Revisiting the classifications of 6d SCFTs and LSTs
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• M String, Monopole String and Modular Forms
• Blowup Equations for 6d SCFTs. I
• Classification of 6d N=(1,0) gauge theories
• A "Lagrangian" for the E7 Superconformal Theory
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• Tinkertoys for the E7 Theory
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• Holography, Brane Intersections and Six-dimensional SCFTs
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• F-Theory on Quotients of Elliptic Calabi-Yau Threefolds
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• The Gravitational Sector of 2d (0,2) F-theory Vacua
• Elliptic Blowup Equations for 6d SCFTs. IV: Matters
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• Matter in transition
• E-string Quantum Curve
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• Testing 5d-6d dualities with fractional D-branes
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• Five-Brane Webs and Highest Weight Representations
• Global tensor-matter transitions in F-theory
• 6D F-theory models and elliptically fibered Calabi-Yau threefolds over semi-toric base surfaces
• Elliptic Quantum Curves of 6d SO(N) theories
• The Characteristic Dimension of Four-dimensional $\mathcal{N}=2$ SCFTs
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• Automatic Enhancement in 6D Supergravity and F-theory Models
• E(lementary) Strings in Six-Dimensional Heterotic F-Theory
• Elliptic Quantum Curves of Class ${\mathcal{S}}_k$
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• RG flows from (1,0) 6D SCFTs to N=1 SCFTs in four and three dimensions
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• Blowup Equations for Little Strings
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• Diagrammatic Expansion of Non-Perturbative Little String Free Energies
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• Geometry of 6D RG Flows
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• 4d N=1 from 6d D-type N=(1,0)
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• Atomic Higgsings of 6D SCFTs
• SCFTs, Holography, and Topological Strings
• Isomorphisms of 4d N=2 SCFTs from 6d
• Punctures and Dynamical Systems
• Large U(1) charges from flux breaking in 4D F-theory models
• Bootstrapping ADE M-strings
• Atomic Higgsings of 6D SCFTs II: Induced Flows
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• Towards natural and realistic $E_7$ GUTs in F-theory
• Affine characters at negative level and elliptic genera of non-critical strings
• Evidence for C-theorems in 6D SCFTs
• B-brane transport in anomalous (2,2) models and localization
• Non-flat elliptic four-folds, three-form cohomology and strongly coupled theories in four dimensions
• EFT of 6D SUSY RG Flows
• Probing Quantum Curves and Transitions in 5d SQFTs via Defects and Blowup Equations
• Orbi-Instantons and Class $\mathcal{S}$ Theories of Type D
• Covariant Fracton Electrodynamics in Six Dimensions
• Geometric Approaches to Quantum Fields and Strings at Strong Couplings
• Non-perturbative Symmetries of Little Strings and Affine Quiver Algebras