Dualities of Adjoint SQCD and Supersymmetry Enhancement

Abstract: We propose a new dual description of four-dimensional $\mathcal{N}=1$ $SU(N)$ gauge theory with one adjoint ($X$) and $N_f$ fundamental matters with a superpotential $W = \text{Tr}\, X^{p+1}$. The dual theory consists of the $\mathcal{D}_p[SU(N)]$ Argyres-Douglas theory coupled to $SU(N)$ gauge theory and $N_f$ fundamentals with a superpotential deformation. We study renormalization group fixed points of the Argyres-Douglas dual theories with and without superpotential deformations, and identify the conditions for them to be dual to the fixed points of adjoint SQCD. We check our proposal via matching central charges, chiral operators and superconformal indices. We find that when $N_f = 2N$ and $p=2$, the dual theory flows to $\mathcal{N}=2$ $SU(N)$ superconformal QCD with $2N$ flavors upon suitable superpotential deformation, exhibiting supersymmetry enhancement.