R-current three-point functions in 4d $\mathcal{N}=1$ superconformal theories
Abstract
In 4d 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 SCFTs.
Cite
@article{arxiv.1804.09717,
title = {R-current three-point functions in 4d $\mathcal{N}=1$ superconformal theories},
author = {Andrea Manenti and Andreas Stergiou and Alessandro Vichi},
journal= {arXiv preprint arXiv:1804.09717},
year = {2019}
}
Comments
39 pages. Ancillary Mathematica file with summary of results included with submission. v2: Typos fixed, references added, minor corrections/additions