SUPERSYMMETRIC LORENTZ INVARIANT DEFORMATIONS OF SUPERSPACES

Abstract

Lorentz invariant supersymmetric deformations of superspaces based on Moyal star product parametrized by Majorana spinor λa and Ramond Grassmannian vector [Formula: see text] in the spinor realization42 are proposed. The map of supergravity background into composite supercoordinates: [Formula: see text] valid up to the second order corrections in deformation parameter h and transforming the background dependent Lorentz noninvariant (anti)commutators of supercoordinates into their invariant Moyal brackets is revealed. We found one of the deformations to depend on the axial vector [Formula: see text] and to vanish for the θ components with the same chiralities. The deformations in the (super)twistor picture are discussed.