Abstract
In this paper we consider nonanticommutative field theories in $\mathcal{N}=2$ superspace formalism on three-dimensional manifolds with a boundary. We modify the original Lagrangian in such a way that it preserves half the supersymmetry even in the presence of a boundary. We also analyze the partial breaking of supersymmetry caused by nonanticommutativity between fermionic coordinates. Unlike in four dimensions, in three dimensions a theory with $\mathcal{N}=1/2$ supersymmetry cannot be obtained by a nonanticommutative deformation of an $\mathcal{N}=1$ theory. However, in this paper we construct a three-dimensional theory with $\mathcal{N}=1/2$ supersymmetry by studying a combination of nonanticommutativity and boundary effects, starting from $\mathcal{N}=2$ supersymmetry.
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