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.

Correcting a few tables and Hasse diagrams, few references added

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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