Quaternionic (super)twistors extensions and general superspaces

TL;DR

This paper constructs 4D N-extended quaternionic superspaces from a graded extension of Penrose-twistor theory, exploring their structure, field content, and implications for supergravity and tensorial central charges.

Contribution

It introduces a novel formulation of quaternionic superspaces for supergravity, extending Penrose-twistor theory with graded structures and analyzing their physical and mathematical properties.

Findings

Defined the structure and coordinates of quaternionic superspaces

Linked superspace components to supergravity field content

Clarified the role of tensorial central charges in this framework

Abstract

In a attempt to treat a supergravity as a tensor representation, the 4-dimensional N-extended quaternionic superspaces are constructed from the (diffeomorphyc)graded extension of the ordinary Penrose-twistor formulation, performed in a previous work of the authors[14], with N = p + k: These quaternionic superspaces have 4 + k (N - k) even-quaternionic coordinates and 4N odd- quaternionic coordinates where each coordinate is a quaternion composed by four C-felds (bosons and fermions respectively). The fields content as the dimensionality (even and odd sectors) of these superspaces are given and exemplified by selected physical cases. In this case the number of felds of the supergravity is determined by the number of components of the tensor representation of the 4-dimensional N-extended quaternionic superspaces. The role of tensorial central charges for any N even USp (N) = Sp (N;HC) \ U (N;HC) is elucidated from this theoretical context.