Super-Yang-Mills theory in SIM(1) superspace

In this paper, we will analyze three-dimensional supersymmetric Yang-Mills theory coupled to matter fields in SIM(1) superspace formalism. The original theory which is invariant under the full Lorentz group has N = 1 supersymmetry. However, when we break the Lorentz symmetry down to SIM(1) group, the SIM(1) superspace will break half the supersymmetry of the original theory. Thus, the resultant theory in SIM(1) superspace will have N = 1/2 supersymmetry. This is the first time that N = 1 supersymmetry will be broken down to N = 1/2 supersymmetry, for a three-dimensional theory, on a manifold without a boundary. This is because it is not possible to use nonanticommutativity to break N = 1 supersymmetry down to N = 1/2 supersymmetry in three dimensions.