# Supersymmetric gauge theories with decoupled operators and chiral ring stability

## TL;DR

This paper introduces a method to complete supersymmetric gauge theories with decoupled operators, enabling consistent computations and dualities, including a novel 3D duality with emergent symmetries.

## Contribution

It proposes a systematic way to handle operators below the unitarity bound and explores dualities and chiral ring stability in supersymmetric theories.

## Key findings

- A new completion method for supersymmetric theories with decoupled operators.
- Establishment of a duality between an $
abla$1$ SU(2)$ gauge theory and the $A_3$ Argyres-Douglas model.
- Identification of a 3D duality with $
abla$4$ SQED with two flavors and emergent global symmetry.

## Abstract

We propose a general way to complete supersymmetric theories with operators below the unitarity bound, adding gauge-singlet fields which 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 [1,2], 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 $\mathcal{N}=4$ 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.