Quaternionic (super) twistors extensions and general superspaces

Abstract

In a attempt to treat a supergravity as a tensor representation, the four-dimensional NN-extended quaternionic superspaces are constructed from the (diffeomorphyc) graded extension of the ordinary Penrose-twistor formulation, performed in a previous work of the authors [D. J. Cirilo-Lombardo and V. N. Pervushin, Int. J. Geom. Methods Mod. Phys., doi: http://dx.doi.org/10.1142/S0219887816501139.], with N=p+k.N=p+k. These quaternionic superspaces have 4+k(N−k)4+k(N−k) even-quaternionic coordinates and 4N4N odd-quaternionic coordinates, where each coordinate is a quaternion composed by four Cℂ-fields (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 fields of the supergravity is determined by the number of components of the tensor representation of the four-dimensional NN-extended quaternionic superspaces. The role of tensorial central charges for any NN even USp(N)=Sp(N,HC)∩U(N,HC)USp(N)=Sp(N,ℍℂ)∩U(N,ℍℂ) is elucidated from this theoretical context.