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