# OPE Selection Rules for Schur Multiplets in 4D $\mathcal{N}=2$ Superconformal Field Theories

## TL;DR

This paper derives explicit OPE selection rules for Schur multiplets in 4D $
N=2$ superconformal field theories, revealing constraints on quantum numbers and advancing understanding of their chiral algebra structure.

## Contribution

It provides the first general expressions for three-point functions involving Schur multiplets and proposes conjectured selection rules for these operators.

## Key findings

- Derived explicit three-point functions for Schur multiplets.
- Established non-trivial quantum number constraints for Schur operators.
- Proposed conjecture for selection rules of general Schur multiplets.

## Abstract

We compute general expressions for two types of three-point functions of (semi-)short multiplets in four-dimensional $\mathcal{N}=2$ superconformal field theories. These (semi-)short multiplets are called "Schur multiplets" and play an important role in the study of associated chiral algebras. The first type of the three-point functions we compute involves two half-BPS Schur multiplets and an arbitrary Schur multiplet, while the second type involves one stress tensor multiplet and two arbitrary Schur multiplets. From these three-point functions, we read off the corresponding OPE selection rules for the Schur multiplets. Our results particularly imply that there are non-trivial selection rules on the quantum numbers of Schur operators in these multiplets. We also give a conjecture on the selection rules for general Schur multiplets.