One can derive a large class of new $\mathcal{ N}=1$ SCFTs by turning on $\mathcal{ N}=1$ preserving deformations for $\mathcal{ N}=2$ Argyres-Dougals theories. In this work, we use $\mathcal{ N}=2$ superconformal indices to get indices of $\mathcal{ N}=1$ SCFTs, then use these indices to derive chiral rings of $\mathcal{ N}=1$ SCFTs. For a large class of $\mathcal{ N}=2$ theories, we find that the IR theory contains only free chirals if we deform the parent $\mathcal{ N}=2$ theory using the Coulomb branch operator with smallest scaling dimension. Our results provide interesting lessons on studies of $\mathcal{ N}=1$ theories, such as $a$-maximization, accidental symmetries, chiral ring, etc.
Categories: hep-th