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 $\mathcal{N}=1$ SU(2) gauge theory and the $\mathcal{N}=2$ $A_3$ Argyres-Douglas theory, mapping the moduli space and chiral ring of the completed $\mathcal{N}=1$ theory to those of the $A_3$ model. We reduce the completed gauge theory to 3D, finding a 3D duality with $\mathcal{N}=4$ supersymmetric QED (SQED) with two flavors. The naive dimensional reduction is instead $\mathcal{N}=2$ SQED. Crucial is a concept of chiral ring stability, which modifies the superpotential and allows for a 3D emergent global symmetry.

• Received 10 August 2017

DOI:https://doi.org/10.1103/PhysRevLett.119.251601