Supersymmetric Lorentz invariant deformations of superspaces

Lorentz invariant supersymmetric deformations of superspaces based on Moyal star product parametrized by Majorana spinor λ a and Ramond grassmannian vector ψ m = − 1 2 (¯ θγ m λ) in the spinor realization [35] are proposed. The map of supergravity background into composite supercoordinates: (B −1 mn , Ψ a m , C ab) ↔ (iψ m ψ n , ψ m λ a , λ a λ b) valid up to the second order corrections in deformation parameter h and transforming the background dependent Lorentz noninvariant (anti)commutators of supercoordi-nates into their invariant Moyal brackets is revealed. We found one of the deformations to depend on the axial vector ψ 1m = 1 2 (¯ θγ m γ 5 λ) and to vanish for the θ components with the same chiralities. The deformations in the (super)twistor picture are discussed.