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Universal properties of superconformal OPEs for 1/2 BPS operators in $3\leq D \leq 6$
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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.
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Superconformal Blocks for Mixed 1/2-BPS Correlators with $SU(2)$ R-symmetry
Explicit superconformal blocks for mixed half-BPS correlators with SU(2) R-symmetry are computed for all contributing multiplets in a dimension-independent way.
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