Superembedding Formalism and Supertwistors

TL;DR

This work demonstrates a precise equivalence between the superembedding and supertwistor formalisms for constructing manifestly covariant correlators in $4$D $\mathcal{N}=1$ SCFTs (and $4$D CFTs when $\mathcal{N}=0$). By exploiting the identification of compactified Minkowski superspace with the manifold $\mathcal{G}$ of null two-dimensional subspaces in supertwistor space, the authors derive a simple tensorial relation that maps embedding-space tensors $X_{AB},\overline{X}^{AB}$ to twistor-space invariants $Y_{ar{i}j}^{\dot{\tilde{c}}\tilde{c}}$. The paper provides an explicit example of a three-point function, showing that results obtained in either framework coincide exactly, thus enabling flexible choice of method for computing SCFT correlators. The findings lay groundwork for systematic tensor classifications to tackle more intricate correlators and highlight the practical value of having both approaches in one’s toolkit for SCFT analyses.

Abstract

We establish a correspondence between superembedding and supertwistor methods for constructing 4D N = 1 SCFT correlation functions by deriving a simple relation between tensors used in the two methods. Our discussion applies equally to 4D CFTs by simply reducing all formulas to the N = 0 case.