Super-Yang-Mills Theory in SIM(1) Superspace

In this paper, we will analyse 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 $\mathcal{N} =1$ 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 $\mathcal{N} =1/2$ supersymmetry. This is the first time that $\mathcal{N} =1 $ supersymmetry will be broken down to $\mathcal{N} =1/2$ supersymmetry, for a three dimensional theory, on a manifold without a boundary. This is because it is not possible to use non-anticommutativity to break $\mathcal{N} =1$ supersymmetry down to $\mathcal{N} =1/2$ supersymmetry in three dimensions.