Argyres-Seiberg Duality and the Higgs Branch

We demonstrate the agreement between the Higgs branches of two ${\mathcal{N}=2}We demonstrate the agreement between the Higgs branches of two N=2{\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 E ₆ flavor symmetry. In mathematical terms, we demonstrate the equivalence between a hyperk?hler quotient of a linear space and another hyperk?hler quotient involving the minimal nilpotent orbit of E ₆, modulo the identification of the twistor lines.