In this paper the SIM (2) superspace formulation of the supersymmetric YangMills gauge theory minimally coupled to chiral superfields is discussed. The super-Poincare invariant supersymmetric Yang-Mills theory is rewritten to SIM (2) superspace formalism and the effects of SIM (2) invariant but Lorentz breaking terms are discussed. Two approaches are investigated. The first is based on the gauge chiral representation of the supersymmetric gauge theory and the second is based on the covariant representation of the supersymmetric gauge theory.
In this paper, we will analyze three-dimensional supersymmetric Yang-Mills theory coupled to matter fields in S1M{ 1) superspace formalism. The original theory which is invariant under the full Lorentz group has AT = 1 supersymmetry. However, when we break the Lorentz symmetry down to SIM( 1) group, the SIM(l) superspace will break half the supersymmetry of the original theory. Thus, the resultant theory in SIM( 1) superspace will have Af = 1/2 supersymmetry. This is the first time that A f = 1 supersymmetry will be broken down to A f = 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 A f = 1 supersymmetry down to A f = 1/2 supersymmetry in three dimensions.
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