Constraints on Chiral Operators in N=2 SCFTs

Understand

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.