Supersymmetric Gauge Theories with Decoupled Operators and Chiral Ring Stability

We propose a general way to complete supersymmetric theories with operators below the unitarity bound, adding gauge-singlet fields that enforce the decoupling of such operators. This makes it possible to perform all usual computations, and to compactify on a circle. We concentrate on a duality between an N=1 SU(2) gauge theory and the N=2 A_{3} Argyres-Douglas theory, mapping the moduli space and chiral ring of the completed N=1 theory to those of the A_{3} model. We reduce the completed gauge theory to 3D, finding a 3D duality with N=4 supersymmetric QED (SQED) with two flavors. The naive dimensional reduction is instead N=2 SQED. Crucial is a concept of chiral ring stability, which modifies the superpotential and allows for a 3D emergent global symmetry.