Abstract
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. Finally, we set the Grassmann coordinates of the Ferrara-Zumino multiplets to zero and extract all three-point functions involving two R-currents and a third conformal primary. Our results pave the way for bootstrapping the correlation function of four R-currents in 4d \( \mathcal{N} \) = 1 SCFTs.
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Manenti, A., Stergiou, A. & Vichi, A. R-current three-point functions in 4d \( \mathcal{N} \) = 1 superconformal theories. J. High Energ. Phys. 2018, 108 (2018). https://doi.org/10.1007/JHEP12(2018)108
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DOI: https://doi.org/10.1007/JHEP12(2018)108