Non-anticommutative ABJ theory

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 N=3 supersymmetry to N=2 supersymmetry. We will then study the ABJ theory in this non-anticommutative superspace. This deformed ABJ theory will be shown to posses N=5 supersymmetry.