Supersymmetric gauge theories with decoupled operators and chiral ring stability

摘要

We propose a general way to complete supersymmetric theories with operatorsbelow the unitarity bound, adding gauge-singlet fields which enforce thedecoupling of such operators. This makes it possible to perform all usualcomputations, and to compactify on a circle. We concentrate on a dualitybetween 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 thecompleted $\mathcal{N}=1$ theory to those of the $A_3$ model. We reduce thecompleted 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, whichmodifies the superpotential and allows for a $3d$ emergent global symmetry.