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

TL;DR

This paper develops supersymmetric Penrose and Witten transforms for 3D superconformal field theories, simplifying the analysis of correlators in twistor space and connecting position and momentum superspaces.

Contribution

It introduces supersymmetric versions of Penrose and Witten transforms for 3D SCFTs with various supersymmetries, deriving explicit correlators and demonstrating the simplicity of extending to higher supersymmetries.

Findings

Derived two and three point functions in superspace using the transforms.

Extended the framework to higher supersymmetries with ease.

Highlighted the simplicity of supertwistors in supersymmetric extensions.

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.