On nonanticommutative N = 2 sigma-models in two dimensions

We study nonanticommutative deformations of script N sign = 2 two-dimensional euclidean sigma models. We find that these theories are described by simple deformations of Zumino's lagrangian and the holomorphic superpotential. Geometrically, this deformation can be interpreted as a fuzziness in target space controlled by the vacuum expectation value of the auxiliary field. In the case of nonanticommutative deformations preserving euclidean invariance, we find that a continuation of the deformed supersymmetry algebra to lorentzian signature leads to a rather intriguing central extension of the ordinary (2,2) superalgebra.