A study of $$ \mathcal{N} $$ = 1 SCFT derived from $$ \mathcal{N} $$ = 2 SCFT: index and chiral ring

Abstract

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