A Foray on SCFT$_3$ via Super Spinor-Helicity and Grassmann Twistor Variables

Abstract

In this paper, we develop a momentum super space formalism for $\mathcal{N}=1,2$ superconformal field theories in three dimensions. First, we solve for super-correlators in the usual momentum superspace variables. However, we found that expressing quantities in super space spinor helicity variables greatly simplifies the analysis. Further, by performing a "half" Fourier transform of the Grassmann coordinates which is analogous to the Twistor transform, an even more remarkable simplification occurs. Using these formalism, we first compute all three point correlation functions involving conserved super-currents with arbitrary spins in $\mathcal{N}=1,2$ theories. We discover interesting double copy relations in $\mathcal{N}=1$ super-correlators. Also, we discovered super double copy relations that take us from $\mathcal{N}=1$ to $\mathcal{N}=2$ super-correlators. We also comment on the connection of our results with the flat space super amplitudes in one higher dimension.