On the OPE of 1/2 BPS Short Operators in N=4 SCFT$_4$

TL;DR

This paper classifies the operator product expansion of 1/2 BPS operators in N=4 superconformal field theory, identifying all protected operators, including BPS and special long multiplets satisfying conservation conditions.

Contribution

It provides a complete classification of protected operators in the OPE of 1/2 BPS operators in N=4 SCFT$_4$, including new long multiplets with conservation properties.

Findings

Identified all possible protected operators in the OPE.

Discovered series of special long multiplets with conservation conditions.

Established selection rules for supermultiplets at the third point.

Abstract

The content of the OPE of two 1/2 BPS operators in N=4 SCFT$_4$ is given by their superspace three-point functions with a third, a priori long operator. For certain 1/2 BPS short superfields these three-point functions are uniquely determined by superconformal invariance. We focus on the cases where the leading ($\theta=0$) components lie in the tensor products $[0,m,0]\otimes[0,n,0]$ and $[m,0,0]\otimes[0,0,n]$ of SU(4). We show that the shortness conditions at the first two points imply selection rules for the supermultiplet at the third point. Our main result is the identification of all possible protected operators in such OPE's. Among them we find not only BPS short multiplets, but also series of special long multiplets which satisfy current-like conservation conditions in superspace.