Current OPEs in Superconformal Theories

Understand

It's well known that in conformal theories the two- and three-point functions of a subset of the local operators-the conformal primaries-suffice, via the operator product expansion (OPE), to determine all local correlation functions of operators.

• It's less well known that, in superconformal theories, the OPE of superdescendants is generally undetermined from those of the superprimaries, and there is no universal notion of superconformal blocks.
• We recall these and related aspects of 4d (S)CFTs, and then we focus on the super operator product expansion (sOPE) of conserved currents in 4d N=1 SCFTs.
• The current-current OPE J(x)J(0) has applications to general gauge mediation.