Super-Penrose $\And$ Witten Transforms for SCFT$_3$

Abstract

The study of three dimensional CFT correlators in twistor space has recently garnered a significant interest. Conformal symmetry acts linearly in the twistor space, which streamlines the analysis. Moreover, twistors provide a connection to the position and momentum space through the Penrose and Witten transforms, respectively. In this work, we develop the supersymmetric versions of Penrose and Witten transforms for three dimensional superconformal field theories for $\mathcal{N}=1\;\textrm{to}\;4$. We derive two and three point functions in the position and momentum superspace for the $\mathcal{N}=1$ scenario using these transforms. Extending this setup to higher supersymmetries turns out to be a simple extension of the $\mathcal{N}=1$ case, which aligns with the inherent simplicity of supertwistors.