Supertwistor realisations of AdS superspaces

TL;DR

This paper develops supertwistor frameworks for AdS superspaces in 3D and 4D, identifying invariant two-point functions and formulating bi-supertwistor and harmonic extensions, advancing superspace geometry understanding.

Contribution

Introduces supertwistor realizations and invariant two-point functions for AdS superspaces, along with bi-supertwistor and harmonic extensions, enhancing geometric and algebraic descriptions.

Findings

Constructed supertwistor realizations for (p,q) AdS superspaces.

Identified invariant two-point functions extending geodesic distances.

Developed bi-supertwistor and harmonic extensions for superspaces.

Abstract

We propose supertwistor realisations of $(p,q)$ anti-de Sitter (AdS) superspaces in three dimensions and $\cal N$-extended AdS superspaces in four dimensions. For each superspace, we identify a two-point function that is invariant under the corresponding isometry supergroup. This two-point function is a supersymmetric extension (of a function) of the geodesic distance. We also describe a bi-supertwistor formulation for $\cal N$-extended AdS superspace in four dimensions and harmonic/projective extensions of $(p,q)$ AdS superspaces in three dimensions.