Constraints on Chiral Operators in N=2 SCFTs

TL;DR

This paper investigates the existence of higher-spin chiral operators in N=2 SCFTs, proving their absence in certain theories and providing a method to determine the 2a-c anomaly from the superconformal index.

Contribution

It offers a superconformal representation theory proof of the non-existence of these operators in specific theories and introduces a way to extract the 2a-c anomaly from the index.

Findings

Higher-spin chiral operators do not exist in Lagrangian and related theories.

The superconformal index can determine the 2a-c conformal anomaly.

Ultraviolet theories with relevant deformations leading to type A theories cannot have these operators.

Abstract

We study certain higher-spin chiral operators in N=2 superconformal field theories (SCFTs). In Lagrangian theories, or in theories related to Lagrangian theories by generalized Argyres-Seiberg-Gaiotto duality ("type A" theories in our classification), we give a simple superconformal representation theory proof that such operators do not exist. This argument is independent of the details of the superconformal index. We then use the index to show that if a theory is not of type A but has an N=2-preserving deformation by a relevant operator that takes it to a theory of this type in the infrared, the ultraviolet theory cannot have these higher-spin operators either. As an application of this discussion, we give a simple prescription to extract the 2a-c conformal anomaly directly from the superconformal index. We also comment on how this procedure works in the holographic limit.