Systematizing semi-shortening

TL;DR

This paper re-derives and generalizes semi-shortening conditions in four-dimensional superconformal field theories, providing a unified framework for BPS operator constraints, especially in $ =4$ super Yang-Mills theory.

Contribution

It introduces a new approach to derive semi-shortening conditions, generalizes them to weaker constraints, and applies these to BPS operators in $ =4$ super Yang-Mills theory.

Findings

Derived semi-shortening conditions using a new method.

Generalized constraints to include all those of Dolan and Osborn.

Provided explicit constraints for BPS operators in $ =4$ super Yang-Mills.

Abstract

We re-derive semi-shortening conditions for four-dimensional superconformal field theory with a different approach. These conditions have similar patterns that can be generalized to weaker constraints, including all those of F. Dolan and H. Osborn. In particular, for the case of $\mathcal{N} = 4$ super Yang-Mills theory, formulated in projective superspace, we find constraints for all BPS operators. We also give an example how constraints can be found from known ones. These constraints are a subset of our maximal set of semi-shortening conditions.