Generalized Faddeev–Popov method for a deformed supersymmetric Yang–Mills theory

In this paper, we will study the deformation of a three dimensional N=2N=2 supersymmetry gauge theory. We will deform this theory by imposing non-anticommutativity. This will break the supersymmetry of the theory from N=2N=2 supersymmetry to N=1N=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 problem will be addressed using a formalism that has been motivated by topological field theories. Finally, we will study the extended BRST symmetry that occurs in this theory.