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

TL;DR

This paper analyzes the operator product expansions of 1/2 BPS superfield operators across various superconformal algebras in dimensions 3 to 6, revealing universal properties and classification of protected operators.

Contribution

It provides a unified framework for understanding OPEs of 1/2 BPS operators in multiple superconformal theories and derives branching rules and classification of protected operators.

Findings

Operators are classified as 1/2 BPS, 1/4 BPS, or semishort.

Three-point functions factorize similarly to superconformal unitary irreducible representations.

Extremal n-point correlators are shown to be non-renormalized.

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.