Argyres-Seiberg Duality and the Higgs Branch

We demonstrate the agreement between the Higgs branches of two 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 super-conformal theory with E-6 flavor symmetry. In mathematical terms, we demonstrate the equivalence between a hyperkahler quotient of a linear space and another hyperkahler quotient involving the minimal nilpotent orbit of E-6, modulo the identification of the twistor lines.