Mir Faizal, Douglas J Smith
In this paper we consider non-anticommutative 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 presence of a boundary. We also analyse the partial breaking of supersymmetry caused by non-anticommutativity between fermionic coordinates. Unlike in four dimensions, in three dimensions a theory with $\mathcal{N} =1/2$ supersymmetry cannot be obtained by a non-anticommutative 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 non-anticommutativity and boundary effects, starting from $\mathcal{N} =2$.
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http://arxiv.org/abs/1211.3654
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