Generalized Faddeev-Popov Method for a Deformed Supersymmetric Yang-Mills Theory

In this paper, we will study the deformation of a three dimensional $\mathcal{N}=2$ supersymmetry gauge theory. We will deform this theory by imposing non-anticommutativity. This will break the supersymmetry of the theory from $\mathcal{N}=2$ supersymmetry to $\mathcal{N}=1$ supersymmetry. We will address the problem that occurs in the Landau gauge due to the existence of multiple solutions to the gauge fixing condition. This will be done by generalizing the Faddeev-Popov method. This formalism is motivated from the Nicolai map in topological field theories. Finally, we will study the extended BRST symmetry that occurs in this theory.