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.
Highlights
In 4d 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 the last decade the conformal bootstrap has been widely used to explore the space of conformal field theories (CFTs), both from a numerical perspective [1] and from an analytical one [2, 3]
Most of these techniques heavily rely on the computation of conformal blocks, or superconformal blocks in the case of superconformal field theories (SCFTs)
Summary
In the last decade the conformal bootstrap has been widely used to explore the space of conformal field theories (CFTs), both from a numerical perspective [1] and from an analytical one [2, 3]. At order θ3θ3 the expansion of the superconformal three-point function contains terms belonging to three-point functions of the schematic form JJ(QQO)p , where Q is the supersymmetric charge and “p” denotes that the operator is conformal primary, and terms belonging to three-point functions of the schematic form JJ(P O) , where P is the generator of translations The latter contributions can be subtracted away using the results of [24], where the specific way contamination from conformal descendants can happen was worked out in generality. A Mathematica file with a summary of all results in attached to this paper as supplementary material
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