Two 6d origins of 4d SCFTs: class $\mathcal{S}$ and 6d (1,0) on a torus

Abstract

We consider all 4d $\mathcal{N}=2$ theories of class $\mathcal{S}$ arising from the compactification of exceptional 6d $(2,0)$ SCFTs on a three-punctured sphere with a simple puncture. We find that each of these 4d theories has another origin as a 6d $(1,0)$ SCFT compactified on a torus, which we check by identifying and comparing the central charges and the flavor symmetry. Each 6d theory is identified with a complex structure deformation of $({\mathfrak{e}}_n,{\mathfrak{e}}_n)$ minimal conformal matter, which corresponds to a Higgs branch renormalization group flow. We find that this structure is precisely replicated by the partial closure of the punctures in the class $\mathcal{S}$ construction. We explain how the plurality of origins makes manifest some aspects of 4d SCFTs, including flavor symmetry enhancements and determining if it is a product SCFT. We further highlight the string theoretic basis for this identification of 4d theories from different origins via mirror symmetry.

54 pages + references, 10 tables, 8 figures, Journal published version

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• 6d Conformal Matter
• S-duality in N=2 supersymmetric gauge theories
• Tinkertoys for Gaiotto Duality
• Anomaly polynomial of general 6d SCFTs
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• Anomaly polynomial of E-string theories
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Cited by in corpus (13)

• Fibrations and Hasse diagrams for 6d SCFTs
• Higgs, Coulomb, and Hall-Littlewood
• Higgs branch RG-flows via Decay and Fission
• The Hitchhiker's Guide to 4d $\mathcal{N}=2$ Superconformal Field Theories
• Infinitely many 4d N=1 SCFTs with a=c
• Trinions for the $3d$ compactification of the $5d$ rank 1 $E_{N_f+1}$ SCFTs
• Atomic Higgsings of 6D SCFTs
• Isomorphisms of 4d N=2 SCFTs from 6d
• Atomic Higgsings of 6D SCFTs II: Induced Flows
• Quiver Polymerisation
• $G_2$-Manifolds from 4d N=1 Theories, Part I: Domain Walls
• Aspects of 4d supersymmetric dynamics and geometry
• Orbi-Instantons and Class $\mathcal{S}$ Theories of Type D