Argyres-Seiberg Duality and the Higgs Branch

We demonstrate the agreement between the Higgs branches of two $${\mathcal{N}=2}$$ theories proposed by Argyres and Seiberg to be S-dual, namely the SU(3) gauge theory with six quarks, and the SU(2) gauge theory with one pair of quarks coupled to the superconformal theory with E6 flavor symmetry. In mathematical terms, we demonstrate the equivalence between a hyperkähler quotient of a linear space and another hyperkähler quotient involving the minimal nilpotent orbit of E6, modulo the identification of the twistor lines.