A study of N =1 SCFT derived from N =2 SCFT: index and chiral ring

TL;DR

This paper uses superconformal indices of $ =2$ theories to analyze $ =1$ SCFTs derived from them, revealing that certain deformations lead to IR theories with only free chiral fields and providing insights into their chiral rings and symmetries.

Contribution

It introduces a method to determine the chiral rings of $ =1$ SCFTs from $ =2$ indices, highlighting the role of Coulomb branch deformations in simplifying IR theories.

Findings

IR theories often contain only free chiral fields after specific deformations

Indices reveal the structure of chiral rings in $ =1$ SCFTs

Deformations using Coulomb branch operators with smallest scaling dimension are significant

Abstract

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.