Conformally compactified Minkowski superspaces revisited

TL;DR

This paper explores alternative supertwistor-based realizations of conformally compactified Minkowski superspaces across various dimensions and supersymmetry extensions, introducing new mathematical frameworks and Fourier expansions.

Contribution

It introduces alternative graded two-form realizations and generalizes constructions to harmonic and projective superspaces for multiple dimensions and supersymmetry levels.

Findings

New supertwistor realizations for superspaces

Generalization to harmonic and projective superspaces

Superconformal Fourier expansion of tensor superfields

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.