Nonanticommutativity in the presence of a boundary.

In this paper we consider nonanticommutative field theories in 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 N=1/2 supersymmetry cannot be obtained by a nonanticommutative deformation of an N=1 theory. However, in this paper we construct a three-dimensional theory with N=1/2 supersymmetry by studying a combination of nonanticommutativity and boundary effects, starting from N=2 supersymmetry