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Article
Report number	arXiv:1804.09717 ; CERN-TH-2018-096
Title	R-current three-point functions in 4d $\mathcal{N}=1$ superconformal theories
Author(s)	Manenti, Andrea (Ecole Polytechnique, Lausanne) ; Stergiou, Andreas (CERN) ; Vichi, Alessandro (Ecole Polytechnique, Lausanne)
Publication	2018-12-18
Imprint	2018-04-25
Number of pages	39
Note	39 pages. Ancillary Mathematica file with summary of results included with submission. v2: Typos fixed, references added, minor corrections/additions
In:	JHEP 12 (2018) 108
DOI	10.1007/JHEP12(2018)108
Subject category	hep-th ; Particle Physics - Theory
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.
Copyright/License	publication: (License: CC-BY-4.0) preprint: (License: arXiv nonexclusive-distrib 1.0)

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