English

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

High Energy Physics - Theory 2019-01-30 v2

Abstract

In 4d N=1\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 N=1\mathcal{N}=1 SCFTs.

Keywords

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

R2 v1 2026-06-23T01:35:50.601Z