Abstract :
In this paper we will discuss non-anticommutative deformations of the harmonic superspace. We will analyse the non-anticommutative deformation of the superspace that break the supersymmetry from image supersymmetry to image supersymmetry. We will then study the ABJ theory in this non-anticommutative superspace. This deformed ABJ theory will be shown to posses image supersymmetry.
