Dualities and phases of 3d$$ \mathcal{N}=1 $$ SQCD

Abstract

Abstract We study gauge theories with $$ \mathcal{N}=1 $$ N = 1 supersymmetry in 2+1 dimensions. We start by calculating the 1-loop effective superpotential for matter in an arbitrary representation. We then restrict ourselves to gauge theories with fundamental matter. Using the 1-loop superpotential, we find a universal form for the phase diagrams of many such gauge theories, which is proven to persist to all orders in perturbation theory using a symmetry argument. This allows us to conjecture new dualities for $$ \mathcal{N}=1 $$ N = 1 gauge theories with fundamental matter. We also show that these dualities are related to results in $$ \mathcal{N}=2 $$ N = 2 supersymmetric gauge theories, which provides further evidence for them.