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

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.

arXiv comment39 pages. Ancillary Mathematica file with summary of results included with submission. v2: Typos fixed, references added, minor corrections/additions

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• Differential operators for superconformal correlation functions
• Correlation functions of spinor current multiplets in $\mathcal{N}=1$ superconformal theory
• Implications of ANEC for SCFTs in four dimensions
• Towards general super Casimir equations for $4D$ $\mathcal{N}=1$ SCFTs
• Superspace invariants and correlators in 4d $\mathcal{N}=1$ superconformal field theories