Classification of all $\mathcal{N}\ge 3$ moduli space orbifold geometries at rank 2

Abstract

We classify orbifold geometries which can be interpreted as moduli spaces of four-dimensional $\mathcal{N}\ge 3$ superconformal field theories up to rank 2 (complex dimension 6). The large majority of the geometries we find correspond to moduli spaces of known theories or discretely gauged version of them. Remarkably, we find 6 geometries which are not realized by any known theory, of which 3 have an $\mathcal{N}=2$ Coulomb branch slice with a non-freely generated coordinate ring, suggesting the existence of new, exotic $\mathcal{N}=3$ theories.

References in corpus (30)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Infinite Chiral Symmetry in Four Dimensions
• Reading between the lines of four-dimensional gauge theories
• The Moduli Space of N=2 SUSY QCD and Duality in N=1 SUSY QCD
• Counting Gauge Invariants: the Plethystic Program
• Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics
• Special Kahler Manifolds
• Central charges of N=2 superconformal field theories in four dimensions
• On the Defect Group of a 6D SCFT
• Vertex operator algebras, Higgs branches, and modular differential equations
• N=3 four dimensional field theories
• S-folds and 4d N=3 superconformal field theories
• Chiral algebras of class S
• On the 6d origin of discrete additional data of 4d gauge theories
• Bootstrapping $\mathcal{N}=3$ superconformal theories
• 4d $\mathcal{N}$=2 theories with disconnected gauge groups
• VOAs labelled by complex reflection groups and 4d SCFTs
• On 4d rank-one N=3 superconformal field theories
• Geometric classification of 4d $\mathcal{N}=2$ SCFTs
• 4d $\mathcal{N}=2$ S-folds
• On S-duality for Non-Simply-Laced Gauge Groups
• Gauge theories from principally extended disconnected gauge groups
• Seiberg-Witten geometries for Coulomb branch chiral rings which are not freely generated
• Free Field Realizations from the Higgs Branch
• Discrete gauge theories of charge conjugation
• On four dimensional N=3 superconformal theories
• The Singularity Structure of Scale-Invariant Rank-2 Coulomb Branches
• 4d $\mathcal{N}=3$ indices via discrete gauging
• Coulomb branches with complex singularities

Cited by in corpus (10)

• New N=2 superconformal field theories from S-folds
• Magnetic quivers for rank 2 theories
• Fibrations and Hasse diagrams for 6d SCFTs
• An N=1 Lagrangian for an N=3 SCFT
• Testing our understanding of SCFTs: a catalogue of rank-2 $\mathcal{N}$=2 theories in four dimensions
• Dirac pairings, one-form symmetries and Seiberg-Witten geometries
• On the compactification of 5d theories to 4d
• The Characteristic Dimension of Four-dimensional $\mathcal{N}=2$ SCFTs
• Macdonald Indices for Four-dimensional $\mathcal{N}=3$ Theories
• Exceptional moduli spaces for exceptional $\mathcal{N}=3$ theories