Conformally compactified Minkowski superspaces revisited

TL;DR

The paper recasts conformally compactified Minkowski superspaces in terms of graded two-forms on dual supertwistor spaces, establishing a bi-supertwistor formulation that naturally extends Dirac's projective lightcone construction to supersymmetric settings. It demonstrates the equivalence of supertwistor and bi-supertwistor realizations in 4D for ${ m N}=1$ and ${ m N}=2$, and generalizes the framework to 4D ${ m N}=2$ harmonic/projective superspace as well as to 3D ${ m N}$-extended harmonic/projective superspaces. A key result is the superconformal Fourier expansion of tensor superfields on the 4D ${ m N}=2$ harmonic/projective space, providing a practical tool for superconformal field theory computations. The work also outlines two equivalent realizations (Type A and B) of the compactified spaces and emphasizes the bi-supertwistor construction as a square root of the standard bi-twistor space, with potential applications to correlation functions and manifestly invariant formulations under the full superconformal group ${ m SU}(2,2|{ m N})$ or ${ m OSp}({ m N}|4,{f R})$ in lower dimensions.

Abstract

Starting from the standard supertwistor realizations for conformally compactified N-extended Minkowski superspaces in three and four space-time dimensions, we elaborate on alternative realizations in terms of graded two-forms on the dual supertwistor spaces. The construction is further generalized to the cases of 4D N=2 and 3D N-extended harmonic/projective superspaces. We present a superconformal Fourier expansion of tensor superfields on the 4D N=2 harmonic/projective superspace.