  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.

High Energy Physics - Theory