Argyres-Seiberg duality and the Higgs branch

TL;DR

This paper verifies the duality between two N=2 supersymmetric theories by showing their Higgs branches are mathematically equivalent, using hyperkähler quotient constructions and twistor line identifications.

Contribution

It provides a mathematical proof of the Higgs branch equivalence for the Argyres-Seiberg dual pair of theories.

Findings

Higgs branches of the dual theories are mathematically equivalent.

Hyperkähler quotient descriptions match for both theories.

Twistor line identification confirms the duality at the geometric level.

Abstract

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 superconformal theory with E_6 flavor symmetry. In mathematical terms, we demonstrate the equivalence between a hyperkaehler quotient of a linear space and another hyperkaehler quotient involving the minimal nilpotent orbit of E_6, modulo the identification of the twistor lines.