• DOI:10.1103/PhysRevD.106.086003
• Corpus ID: 235605928

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

@article{Baume2021Two6O,
  title={Two 6d origins of 4d SCFTs: class \$\mathcal\{S\}\$ and 6d (1,0) on a torus},
  author={Florent Baume and Monica Jinwoo Kang and Craig Lawrie},
  journal={arXiv: High Energy Physics - Theory},
  year={2021}
}

• F. Baume, M. Kang, C. Lawrie
• Published 22 June 2021
• Mathematics
• arXiv: High Energy Physics - Theory

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.