R-current three-point functions in 4d $\mathcal{N}=1$ superconformal theories

Understand

In 4d $\mathcal{N}=1$ superconformal field theories (SCFTs) the R-symmetry current, the stress-energy tensor, and the supersymmetry currents are grouped into a single object, the Ferrara-Zumino multiplet.

• In this work we study the most general form of three-point functions involving two Ferrara-Zumino multiplets and a third generic multiplet.
• We solve the constraints imposed by conservation in superspace and show that non-trivial solutions can only be found if the third multiplet is R-neutral and transforms in suitable Lorentz representations.
• In the process we give a prescription for counting independent tensor structures in superconformal three-point functions.