Universal properties of superconformal OPEs for 1/2 BPS operators in $3\leq D \leq 6$

TL;DR

The paper develops a universal, group-theoretic framework to study the OPEs of 1/2 BPS operators across D=3–6 superconformal algebras, showing that three-point functions factorize into supersingleton-based structures. This leads to simple branching rules for primary superfields and a clear classification of protected operators (1/2 BPS, 1/4 BPS, or semishort) appearing in OPEs. By analyzing the selection rules for two 1/2 BPS insertions, the authors identify when the third operator is protected or can acquire anomalous dimensions, and they apply these insights to non-renormalization of extremal n-point correlators. The work provides a unifying perspective that connects harmonic superspace, supersingleton composites, and the protection mechanism in a way that extends beyond D=4 and highlights implications for AdS/CFT correspondences.

Abstract

We give a general analysis of OPEs of 1/2 BPS superfield operators for the $D=3,4,5,6$ superconformal algebras OSp(8/4,R), PSU(2,2), F${}_4$ and OSp($8^*/4$) which underlie maximal AdS supergravity in $4\leq D+1\leq 7$. \\ The corresponding three-point functions can be formally factorized in a way similar to the decomposition of a generic superconformal UIR into a product of supersingletons. This allows for a simple derivation of branching rules for primary superfields. The operators of protected conformal dimension which may appear in the OPE are classified and are shown to be either 1/2 or 1/4 BPS, or semishort. As an application, we discuss the "non-renormalization" of extremal $n$-point correlators.